Exhibit 10.5 AMENDMENT NO. 3 TO SECOND AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP OF MARTIN MIDSTREAM PARTNERS L.P.

This Amendment No. 3 to the Second Amended and Restated Agreement of Limited Partnership (this “Amendment”) of Martin Midstream Partners L.P., a Delaware limited partnership (the “Partnership”), is executed effective as of the 2^nd day of October, 2012, by Martin Midstream GP LLC, a Delaware limited liability company (the “General Partner”), as the sole general partner of the Partnership. Capitalized terms used herein but not defined shall have the meanings given them in that certain Second Amended and Restated Agreement of Limited Partnership, dated as of November 25, 2009 (as heretofore amended, the “Partnership Agreement”);

WHEREAS, Section 13.1(d)(i) of the Partnership Agreement provides that the General Partner, without the approval of any Partner or Assignee, may amend any provision of the Partnership Agreement and execute, swear to, acknowledge, deliver, file and record whatever documents may be required in connection therewith, to reflect, a change that, in the discretion of the General Partner, does not adversely affect the Limited Partners (including any particular class of Partnership Interests as compared to other classes of Partnership Interests) in any material respect; and  

WHEREAS, acting pursuant to the authority granted to it under Section 13.1(d)(i) of the Partnership Agreement, the General Partner has determined that the following amendments to the Partnership Agreement do not adversely affect the Limited Partners (including any particular class of Partnership Interests as compared to other classes of Partnership Interests) in any material respect.

NOW, THEREFORE, the General Partner, pursuant to Article XIII of the Partnership Agreement, hereby amends the Partnership Agreement as follows:

1.Section 6.1(c)(i) of the Partnership Agreement is hereby amended to add new provisos at the end of Section 6.1(c)(i) as follows:

provided, however, (x) any Net Termination Gain recognized (but not including any Net Termination Gain deemed recognized pursuant to Section 5.5(d)) and otherwise allocable to the holders of the Incentive Distribution Rights pursuant to Sections 6.1(c)(i)(E), (F) and (G) shall be reduced by an amount equal to the difference between $18,000,000 and the aggregate amount of all prior and current distribution reductions made with respect to the holders of the Incentive Distribution Rights pursuant to Section 6.4(c), as determined by the General Partner in its sole discretion, and (y) the amounts of the reduction pursuant to the preceding clause (x) of Net Termination Gain allocable to the holders of the Incentive Distribution Rights shall be allocated 100% to the Unitholders, Pro Rata.

provided, further, the General Partner shall have reasonable discretion to adjust allocations made pursuant to this Section 6.1(c) as between the holders of Incentive Distribution Rights and the other Partners to minimize any economic distortions that might otherwise result based upon any adjustments to distributions made or to be made pursuant Section 6.4(c).

2.Section 6.1(c)(iii) of the Partnership Agreement is hereby deleted in its entirety.

3.Section 6.4 of the Partnership Agreement is hereby amended to add a new clause (c) as follows:

(c)    Notwithstanding anything to the contrary in this Section 6.4, the aggregate distributions otherwise payable to the holders of the Incentive Distribution Rights pursuant to clauses (v), (vi) and (vii) of Section 6.4(a) and clauses (iii), (iv) and (v) of Section 6.4(b) beginning on October 2, 2012 shall be reduced to zero until such time as the aggregate amount of such reductions equals $18,000,000. The amount that would, but for the preceding sentence, be paid to the holders of Incentive Distribution Rights will be distributed 100% to the Unitholders, Pro Rata; provided that any distributions made to the Unitholders pursuant to this Section 6.4(c) with respect to a Quarter shall be deemed to have been distributed to the holders of Incentive Distribution Rights solely for the purpose of determining the amount of any further distributions payable to the holders of Incentive Distribution Rights pursuant to clauses (v), (vi) and (vii) of Section 6.4(a) and clauses (iii), (iv) and (v) of Section 6.4(b) for such Quarter.

4.General Authority. The appropriate officers of the General Partner are hereby authorized to make such further clarifying and conforming changes they deem necessary or appropriate, and to interpret the Partnership Agreement, to give effect to the intent and purpose of this Amendment.

5.Ratification of Partnership Agreement. Except as expressly modified and amended herein, all of the terms and conditions of the Partnership Agreement shall remain in full force and effect.

6.Governing Law. This Amendment will be governed by and construed in accordance with the laws of the State of Delaware.

IN WITNESS WHEREOF, the General Partner has executed this Amendment as of the date first above written.

GENERAL PARTNER:

MARTIN MIDSTREAM GP LLC

By:      /s/ Robert D. Bondurant                    

Name:    Robert D. Bondurant

Title:    Executive Vice President