Exhibit 4.1

SECOND AMENDED AND RESTATED

CERTIFICATE OF DESIGNATIONS

OF

SERIES A CUMULATIVE REDEEMABLE PREFERRED STOCK

OF

POSTROCK ENERGY CORPORATION

POSTROCK ENERGY CORPORATION, a corporation organized and existing under the General Corporation Law of the State of Delaware (the “Corporation”), in accordance with the provisions of Sections 103 and 151 thereof, DOES HEREBY CERTIFY:

The board of directors of the Corporation (the “Board of Directors”), in accordance with the provisions of the certificate of incorporation and the Bylaws of the Corporation and applicable law, at a meeting duly called and held on December 7, 2012, and the holders of a majority of the outstanding shares of Series A (as defined below) by written consent, adopted the following resolution amending and restating, effective on the date this Second Amended and Restated Certificate of Designations of Series A is filed in the office of the Secretary of State of the State of Delaware, the provisions of the Certificate of Designations of Series A Redeemable Preferred Stock:

RESOLVED, that pursuant to the authority vested in the Board of Directors and in accordance with the provisions of the certificate of incorporation of the Corporation and applicable law, a series of Preferred Stock, par value $0.01 per share, of the Corporation be and hereby is created, and that the designation and number of shares of such series, and the voting and other powers, preferences and relative, participating, optional or other rights, and the qualifications, limitations and restrictions thereof (in addition to those set forth in the certificate of incorporation of the Corporation that are applicable to Preferred Stock of all series), of the shares of such series, are as follows:

Section 1. Designation. The distinctive serial designation of such series of Preferred Stock is “Series A Cumulative Redeemable Preferred Stock” (“Series A”). Each share of Series A shall be identical in all respects to every other share of Series A.

Section 2. Number of Shares. The authorized number of shares of Series A shall be 7,250. Shares of Series A that are redeemed, purchased or otherwise acquired by the Corporation, or converted into another series of Preferred Stock, shall be cancelled and retired and revert to authorized but unissued shares of Preferred Stock (provided that any such cancelled shares of Series A may be reissued only as shares of any series other than Series A).

Section 3. Definitions. As used herein with respect to Series A:

(a) “Additional Directors” has the meaning set forth in Section 10.

(b) “Bylaws” means the bylaws of the Corporation, as they may be amended from time to time.

(c) “Business Day” means a day that is a Monday, Tuesday, Wednesday, Thursday or Friday and is not a day on which banking institutions in Oklahoma City, Oklahoma or New York, New York generally are authorized or obligated by law, regulation or executive order to close.

(d) “Certificate of Designations” means this Second Amended and Restated Certificate of Designations relating to the Series A, as it may be amended from time to time.

(e) “Certification of Incorporation” means the certificate of incorporation of the Corporation, as it may be amended from time to time, and shall include this Certificate of Designations.

(f) “Change of Control” means the occurrence of any of the following events:

(i) the sale, lease or transfer, in one transaction or a series of related transactions, of all or substantially all of the Corporation’s assets (determined on a consolidated basis) to any “person” or “group” (as such terms are used in Section 13(d)(3) of the Exchange Act) other than a Wholly Owned Subsidiary; provided, however, that a transaction covered by this clause (i) shall not be a Change of Control if a Specified Person is a party in the transaction; or

(ii) the consolidation or merger of the Corporation with or into any other Person or the merger of another Person with or into the Corporation, pursuant to which the holders of 100% of the total voting power of the total outstanding capital stock of the Corporation immediately prior to the consummation of such consolidation or merger do not beneficially own (within the meaning of Rule 13d-3 of the Exchange Act) in the aggregate more than 50% of the total voting power of the total outstanding capital stock of the continuing or surviving Person immediately after such transaction; provided, however, that a transaction covered by this clause (ii) shall not be a Change of Control if the parties to such transaction include a Specified Person; or

(iii) the acquisition, directly or indirectly, by any “person” or “group” (as such terms are used in Section 13(d)(3) of the Exchange Act), other than White Deer Energy, L.P. or its affiliates, of beneficial ownership (as defined in Rule 13d-3 under the Exchange Act) of more than 20% of the total voting power of the total outstanding capital stock of the Corporation; provided, however, that a transaction covered by this clause (iii) shall not be a Change of Control if the party from whom such stock is acquired in such acquisition is a Specified Person or if a Specified Person has in the aggregate beneficial ownership, immediately prior to such acquisition, of a percentage of the total outstanding capital stock of the Corporation greater than 25%; or

(iv) the first day on which a majority of the individuals who constitute the entire Board of Directors (excluding any Additional Directors) shall not be Continuing Directors.

(g) “Change of Control Payment Date” has the meaning set forth in Section 7(b)(ii).

(h) “Change of Control Price” has the meaning set forth in Section 7(f).

(i) “Common Stock” means the common stock, par value $0.01 per share, of the Corporation.

(j) “Continuing Directors” means individuals (i) who are directors of the Corporation on September 21, 2010 (“Incumbent Directors”), (ii) whose nomination for election or election to the Board of Directors was approved by a majority of the Incumbent Directors then still in office, or (iii) whose nomination for election or election to the Board of Directors was approved by a majority of the Incumbent Directors and the directors approved pursuant to clause (ii) then still in office.

(k) “Default” means (i) after December 31, 2014, the Corporation’s failure to pay in cash any dividend on the applicable Dividend Payment Date in accordance with Section 4 of this Certificate of Designations or (ii) any action or failure to act by the Corporation in violation of Section 6(a), Section 7 or Section 9.

(l) “Dividend Payment Date” means each September 30, December 31, March 31 and June 30, commencing on December 31, 2010.

(m) “Dividend Period” has the meaning set forth in Section 4(a).

(n) “Dividend Record Date” has the meaning set forth in Section 4(a).

(o) “Exchange Act” means the Securities Exchange Act of 1934, as amended, and the rules and regulations promulgated thereunder.

(p) “Junior Stock” means the Common Stock, Series B and any other class or series of stock of the Corporation (other than Series A) that ranks junior to Series A either or both as to the payment of dividends and/or as to the distribution of assets on any liquidation, dissolution or winding up of the Corporation.

(q) “Liquidation Preference” means, with respect to each share of Series A, on any date of determination, the sum of (i) $10,000 and (ii) the accrued and unpaid dividends thereon (including, if applicable as provided in Section 4(a), dividends on such amount), whether or not declared, to such date.

(r) “Original Issue Date” means the date of issuance of any share of Series A.

(s) “Person” means any individual, corporation, limited liability company, partnership, joint venture, association, joint stock company, trust, unincorporated organization, or government or any agency or political subdivision thereof.

(t) “Preferred Stock” means any and all series of preferred stock, par value $0.01 per share, of the Corporation, including the Series A and Series B.

(u) Purchase Agreement” means (i) the Securities Purchase Agreement, dated as of September 2, 2010, as amended from time to time, between the Corporation, White Deer Energy

L.P., White Deer Energy TE L.P. and White Deer Energy FI L.P., including all schedules and exhibits thereto, (ii) the Securities Purchase Agreement, dated as of August 1, 2012, as amended from time to time, between the Corporation, White Deer Energy L.P., White Deer Energy TE L.P. and White Deer Energy FI L.P., including all schedules and exhibits thereto, or (iii) the Securities Purchase Agreement, dated as of December 17, 2012, as amended from time to time, between the Corporation, White Deer Energy L.P., White Deer Energy TE L.P. and White Deer Energy FI L.P., including all schedules and exhibits thereto.

(v) “Series B” means the Corporation’s Preferred Stock designated as “Series B Voting Preferred Stock.”

(w) “Series B Certificate” means the Certificate of Designations of Series B Voting Preferred Stock relating to the Series B, as it may be amended from time to time.

(x) “Specified Person” means White Deer Energy L.P. or any of its affiliates.

(y) “Warrants” means the Warrants to purchase shares of Common Stock, issued pursuant to a Purchase Agreement, including Section 1.4 thereof.

(z) “Wholly Owned Subsidiary” means any subsidiary of the Corporation to the extent that all of the securities of any class or classes of capital stock of such subsidiary entitling the holders thereof (whether at all times or at the times that such class of capital stock has voting power by reason of the happening of any contingency) to vote in the election of members of the board of directors or comparable body of such subsidiary are owned directly or indirectly by the Corporation.

Section 4. Dividends.

(a) Rate. Holders of Series A shall be entitled to receive, on each share of Series A, out of funds legally available for the payment of dividends under Delaware law, cumulative cash dividends at a per annum rate of 12% on the Liquidation Preference. Such dividends shall begin to accrue and be cumulative from the Original Issue Date of such share, shall compound on each Dividend Payment Date (i.e., no dividends shall accrue on other dividends unless and until the first Dividend Payment Date for such other dividends has passed without such other dividends having been paid on such date), and shall be payable in arrears (as provided in this Section 4(a)). Through December 31, 2014, dividends shall be payable only when, as and if declared by the Board of Directors. Thereafter, the Board of Directors shall declare dividends, payable on each Dividend Payment Date, subject only to the legal availability of funds for declaration and payment thereof. If any such Dividend Payment Date would otherwise occur on a day that is not a Business Day, such Dividend Payment Date shall instead be (and any dividend payable on Series A on such Dividend Payment Date shall instead be payable on) the immediately succeeding Business Day with the same force and effect as if made on such Dividend Payment Date. The amount of dividends payable on the Series A shall be computed on the basis of a 360-day year consisting of twelve 30-day months, and with respect to any date of determination that is not a Dividend Payment Date, actual days elapsed over a 30-day month.

Dividends that are payable on Series A on any Dividend Payment Date shall be payable to holders of record of Series A as they appear on the stock register of the Corporation on the

applicable record date, which shall be the 15th calendar day before such Dividend Payment Date (as originally scheduled) or such other record date fixed by the Board of Directors that is not more than 60 nor less than 10 days prior to such Dividend Payment Date (each, a “Dividend Record Date”). Any such day that is a Dividend Record Date shall be a Dividend Record Date whether or not such day is a Business Day.

Each dividend period (a “Dividend Period”) shall commence on the calendar day immediately following a Dividend Payment Date (other than the initial Dividend Period with respect to any share of Series A, which shall commence on and include the Original Issue Date of such share) and shall end on and include the next Dividend Payment Date. Dividends payable in respect of a Dividend Period shall be payable in arrears on the Dividend Payment Date ending such Dividend Period.

(b) Priority of Dividends. When dividends are not paid (or declared and a sum sufficient for payment thereof set aside for the benefit of the holders thereof on the applicable Dividend Record Date) on any Dividend Payment Date in full upon the Series A, all dividends declared on the Series A and payable on such Dividend Payment Date shall be declared pro rata so that the respective amounts of such dividends declared shall bear the same ratio to each other as all accrued and unpaid dividends per share on the Series A (including, if applicable as provided in Section 4(a) above, dividends on such amount) bear to each other.

Section 5. Liquidation Rights.

(a) Voluntary or Involuntary Liquidation. In the event of any liquidation, dissolution or winding up of the affairs of the Corporation, whether voluntary or involuntary, holders of Series A shall be entitled to receive for each share of Series A, out of the assets of the Corporation or proceeds thereof (whether capital or surplus) available for distribution to stockholders of the Corporation, and after satisfaction of all liabilities and obligations to creditors of the Corporation, before any distribution of such assets or proceeds is made to or set aside for the holders of Common Stock and any other Junior Stock, payment in full in an amount equal to the Liquidation Preference of such share.

(b) Partial Payment. If in any distribution described in Section 5(a) above, the assets of the Corporation or proceeds thereof are not sufficient to pay the Liquidation Preferences in full to all holders of Series A as to such distribution, the amounts paid to the holders of Series A shall be paid pro rata in accordance with the respective aggregate Liquidation Preferences of the holders of Series A.

(c) Residual Distributions. If the Liquidation Preference has been paid in full to all holders of Series A, the holders of other stock of the Corporation shall be entitled to receive all remaining assets of the Corporation (or proceeds thereof) according to their respective rights and preferences.

(d) Merger, Consolidation and Sale of Assets Not Liquidation. For purposes of this Section 5, the merger or consolidation of the Corporation with any other corporation or other entity, including a merger or consolidation in which the holders of Series A receive cash, securities or other property for their shares, or the sale, lease or exchange (for cash, securities or other property) of all or substantially all of the assets of the Corporation, shall not constitute a liquidation, dissolution or winding up of the Corporation, but shall be governed by Section 7.

Section 6. Redemption.

(a) Mandatory Redemption. On March 21, 2018, the Corporation shall redeem, in whole, the shares of Series A at the time outstanding, upon notice given as provided in Section 6(c) below, at a redemption price per share equal to 100% of the Liquidation Preference of such share as of the redemption date. The redemption price for any shares of Series A shall be payable on the redemption date to the holder of such shares against surrender of the certificate(s) evidencing such shares to the Corporation or its agent.

(b) Optional Redemption. From and after one year from the Original Issue Date until March 21, 2018, the Corporation, at its option, may redeem, in whole at any time or in part from time to time, the shares of Series A at the time outstanding, upon notice given as provided in Section 6(c) below, at a redemption price per share equal to 110% of the Liquidation Preference of such share as of the redemption date, provided that the minimum number of shares of Series A redeemable at any time is the lesser of (i) 500 shares of Series A and (ii) the number of shares of Series A outstanding. The redemption price for any shares of Series A shall be payable on the redemption date to the holder of such shares against surrender of the certificate(s) evidencing such shares to the Corporation or its agent.

(c) Notice of Redemption. Notice of every redemption of shares of Series A shall be given to the holders of record of the shares to be redeemed at their respective last addresses appearing on the books of the Corporation. Such mailing shall be at least 30 days and not more than 60 days before the date fixed for redemption. Any notice mailed as provided in this Subsection shall be conclusively presumed to have been duly given, whether or not the holder receives such notice, but failure duly to give such notice by mail, or any defect in such notice or in the mailing thereof, to any holder of shares of Series A designated for redemption shall not affect the validity of the proceedings for the redemption of any other shares of Series A. Each notice of redemption given to a holder shall state: (1) the redemption date; (2) the number of shares of Series A to be redeemed and, if less than all the shares held by such holder are to be redeemed, the number of such shares to be redeemed from such holder; (3) the redemption price; and (4) the place or places where certificates for such shares are to be surrendered for payment of the redemption price.

(d) Partial Redemption. In case of any redemption of part of the shares of Series A at the time outstanding, the shares to be redeemed shall be selected pro rata among holders of the Series A. If fewer than all the shares represented by any certificate are redeemed, a new certificate shall be issued representing the unredeemed shares without charge to the holder thereof.

(e) Effectiveness of Redemption. If notice of redemption has been duly given and if on or before the redemption date specified in the notice all funds necessary for the redemption have been deposited by the Corporation, in trust for the pro rata benefit of the holders of the shares called for redemption, with a bank or trust company doing business in the Borough of Manhattan, The City of New York, and having a capital and surplus of at least $500 million and

selected by the Board of Directors, so as to be and continue to be available solely therefor, then, notwithstanding that any certificate for any share so called for redemption has not been surrendered for cancellation, on and after the redemption date dividends shall cease to accrue on all shares so called for redemption, all shares so called for redemption shall no longer be deemed outstanding and all rights with respect to such shares shall forthwith on such redemption date cease and terminate, except only the right of the holders thereof to receive the amount payable on such redemption from such bank or trust company, without interest. Any funds unclaimed at the end of three years from the redemption date shall, to the extent permitted by law, be released to the Corporation, after which time the holders of the shares so called for redemption shall look only to the Corporation for payment of the redemption price of such shares.

Section 7. Offer to Purchase Upon a Change of Control.

(a) In connection with the occurrence of a Change of Control, the Corporation shall make an offer to purchase all of the shares of Series A outstanding (a “Change of Control Offer”) on the terms set forth in this Section 7. The Change of Control Offer shall be made in compliance with all applicable laws, including, without limitation (if applicable), Regulation 14E and 14D under the Exchange Act and the rules thereunder and all other applicable Federal and state securities laws. To the extent that the provisions of any securities laws or regulations conflict with the provisions of this Section 7, the Corporation shall comply with the applicable securities laws and regulations and shall not be deemed to have breached its obligations under this Section 7 by virtue thereof.

(b) No sooner than fifteen (15) days and within that time period, as soon as reasonably practicable, prior to the consummation, or anticipated consummation, of a Change of Control, the Corporation shall commence the Change of Control Offer by mailing to each holder of shares of Series A a notice, which shall govern the terms of the Change of Control Offer, and shall state:

(i) that the Change of Control Offer is being made pursuant to this Section 7 and that all shares of Series A tendered will be accepted for payment subject to the consummation of the Change of Control;

(ii) the Change of Control Price (as defined below) and the date until which the Corporation may accept for payment shares of Series A (the “Change of Control Payment Date”), which shall be (subject to consummation of the Change of Control) no later than forty-five (45) days after the date the Change of Control occurs;

(iii) that any shares of Series A not tendered for payment pursuant to the Change of Control Offer shall continue to accrue dividends and be redeemable in accordance with the terms hereof;

(iv) that, unless the Corporation defaults in the payment of the Change of Control Price, all shares of Series A accepted for payment pursuant to the Change of Control Offer shall cease to accrue dividends on the Change of Control Payment Date;

(v) that any holder electing to have certificates representing shares of Series A pursuant to a Change of Control Offer shall be required to surrender such certificates representing shares of Series A to the Corporation or its designated agent at the address specified in the notice prior to the close of business on the Change of Control Payment Date;

(vi) that any holder of a share of Series A shall be entitled to withdraw such election if the Corporation or its designated agent receives, not later than the close of business on the Change of Control Payment Date, a telegram, telex, facsimile transmission or letter setting forth the name of the holder of such shares of Series A, the number of shares of Series A such holder delivered for purchase, and a statement that such holder is withdrawing its election to have such shares of Series A purchased;

(vii) that a holder whose shares of Series A are being purchased only in part shall be issued new shares of Series A for the unpurchased shares of Series A represented by any certificate surrendered;

(viii) the instructions that holders must follow in order to tender their shares of Series A; and

(ix) the circumstances and relevant facts regarding such Change of Control.

(c) On the Change of Control Payment Date, the Corporation shall, to the extent of funds legally available therefore and otherwise lawful, accept for payment the shares of Series A tendered and not withdrawn pursuant to the Change of Control Offer. The Corporation shall promptly mail to each holder of shares of Series A so accepted payment (or pay in person any holder presenting itself at the Corporation) in an amount equal to the purchase price for such shares, and the unpurchased shares of Series A surrendered, if any.

(d) The Corporation shall make a public announcement of the results of the Change of Control Offer on or as soon as practicable after the Change of Control Payment Date.

(e) The Corporation shall not enter into any agreement providing for a Change of Control unless the agreement permits the Corporation or any successor entity to comply with the provisions hereof.

(f) “Change of Control Price” means an amount of cash per share of Series A equal to 110% of the Liquidation Price of such share as of the date of acceptance for payment.

Section 8. Conversion. Holders of Series A shares shall have no right to exchange or convert such shares into any other securities.

Section 9. Voting Rights.

(a) General. The holders of Series A shall not have any voting rights except as set forth below or as otherwise from time to time required by law.

(b) Voting Rights as to Particular Matters.

(i) So long as any shares of Series A are outstanding, in addition to any other vote or consent of stockholders required by law or by the Certificate of Incorporation, the vote or

consent of the holders of a majority of the shares of Series A at the time outstanding and entitled to vote thereon, given in person or by proxy, either in writing without a meeting or by vote at any meeting called for the purpose, shall be necessary for effecting or validating:

(A) Any amendment, alteration or repeal of any provision of the Certificate of Incorporation so as to change the rights, preferences, privileges or voting powers of the Series A;

(B) Any amendment or alteration of the Certificate of Incorporation to authorize or create, or increase or decrease the authorized amount of, any shares of Series A, or the issuance of any shares of Series A;

(C) Any amendment or alteration of the Certificate of Incorporation to authorize or create, or increase the authorized amount of, any shares of any class or series of capital stock of the Corporation ranking pari passu with or senior to the Series A with respect to either or both the payment of dividends or the distribution of assets on any liquidation, dissolution or winding up of the Corporation;

(D) Any amendment, alteration or repeal of any provision of the Certificate of Incorporation or Bylaws so as to adversely affect the special rights, preferences, privileges or voting powers of the Series A;

(E) Any declaration or payment of cash dividends on any Common Stock or other Junior Stock;

(F) Any redemption or repurchase of any shares of any class or series of capital stock of the Corporation, other than the Series A and any shares of Common Stock withheld by the Corporation to pay taxes upon the granting or vesting of awards to any of its employees under any equity compensation plan of the Corporation;

(G) Any increase in the size of the Board of Directors, except as set forth in Section 10(i);

(H) Any material change in the Corporation’s business as conducted on the Original Issue Date;

provided, however, that the transactions contemplated in the Series B Certificate and the Warrant shall be permitted without any vote or consent of the holders of shares of Series A.

(c) Procedures for Voting and Consents. The rules and procedures for calling and conducting any meeting of the holders of Series A (including, without limitation, the fixing of a record date in connection therewith), the solicitation and use of proxies at such a meeting, the obtaining of written consents and any other aspect or matter with regard to such a meeting or such consents shall be governed by any rules of the Board of Directors, in its discretion, may adopt from time to time, which rules and procedures shall conform to the requirements of the Certificate of Incorporation, the Bylaws, and applicable law and the rules of any national securities exchange or other trading facility on which the Series A is listed or traded at the time. Whether the vote or consent of the holders of a plurality, majority or other portion of the shares of Series A has been cast or given on any matter on which the holders of shares of Series A are entitled to vote shall be determined by the Corporation by reference to the Liquidation Preference of the shares voted or covered by the consent.

Section 10. Default. Upon the occurrence of a Default, if such Default shall not have been cured within thirty (30) days after the date on which the holders of a majority of the Series A give written notice of such Default to the Corporation:

(i) the holders of a majority of the Series A shall have the right to elect two additional directors to the Board of Directors (the “Additional Directors”) to serve until the date on which such Default is cured or waived by the holders of Series A; provided that the number of any Additional Directors shall not exceed two at any time regardless of the occurrence of one or more Defaults; and

(ii) the dividend rate shall increase by 2.00% from and including the date on which the Default occurred and be continuing through but excluding the date on which the Default is cured or waived by the holders of Series A; provided that any increase in the dividend rate shall not exceed 2.00% at any time, regardless of the number of Defaults.

Section 11. Record Holders. To the fullest extent permitted by applicable law, the Corporation may deem and treat the record holder of any share of Series A as the true and lawful owner thereof for all purposes, and the Corporation shall not be affected by any notice to the contrary.

Section 12. Notices. All notices or communications in respect of Series A shall be sufficiently given if given in writing and delivered in person or by fax, overnight or certified mail, or if given in such other manner as may be permitted in this Certificate of Designations, in the Certificate of Incorporation or Bylaws or by applicable law.

Section 13. No Preemptive Rights. No share of Series A shall have any rights of preemption whatsoever as to any securities of the Corporation, or any warrants, rights or options issued or granted with respect thereto, regardless of how such securities, or such warrants, rights or options, may be designated, issued or granted.

Section 14. Replacement Certificates. The Corporation shall replace any mutilated certificate at the holder’s expense upon surrender of that certificate to the Corporation. The Corporation shall replace certificates that become destroyed, stolen or lost at the holder’s expense upon delivery to the Corporation of reasonably satisfactory evidence that the certificate has been destroyed, stolen or lost, together with any indemnity that may be reasonably required by the Corporation.

Section 15. Other Rights. The shares of Series A shall not have any rights, preferences, privileges or voting powers or relative, participating, optional or other special rights, or qualifications, limitations or restrictions thereof, other than as set forth herein or in the Certificate of Incorporation or as provided by applicable law.

In Witness Whereof, POSTROCK ENERGY CORPORATION has caused this certificate to be signed this 18th day of December, 2012.