Exhibit (l)(2)

JONES DAY

2727 NORTH HARWOOD STREET • DALLAS, TEXAS 75201.1515

TELEPHONE: +1.214.220.3939 • FACSIMILE: +1.214.969.5100

December 15, 2017

Capital Southwest Corporation

5400 Lyndon B. Johnson Freeway, Suite 1300

Dallas, Texas 75240

Re: $57,500,000 Aggregate Principal Amount of

5.95% Notes due 2022 of Capital Southwest Corporation

Ladies and Gentlemen:

We are acting as counsel for Capital Southwest Corporation, a Texas corporation (“CSWC”), in connection with the issuance and sale of $57,500,000 in aggregate principal amount of 5.95% Notes due 2022 (the “Notes”) of CSWC (including up to $7,500,000 in Notes issuable pursuant to an option granted to the underwriters in the offering of the Notes), pursuant to the Underwriting Agreement, dated as of December 12, 2017 (the “Underwriting Agreement”), entered into by and between CSWC and Keefe, Bruyette & Woods, Inc., acting as representative of the several underwriters named therein. The Notes are being issued under an indenture (the “Base Indenture”), by and between the Company and U.S. Bank National Association, as trustee (the “Trustee”), as supplemented by the First Supplemental Indenture (together with the Base Indenture, the “Indenture”), by and between the Company and the Trustee.

In connection with the opinion expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of such opinion. Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that the Notes constitute valid and binding obligations of CSWC.

For purposes of the opinion expressed herein, we have assumed that (i) the Trustee has authorized, executed and delivered the Indenture, (ii) the Notes have been duly authenticated by the Trustee in accordance with the Indenture and (iii) the Indenture is the valid, binding and enforceable obligation of the Trustee.

The opinion expressed herein is limited by (i) bankruptcy, insolvency, reorganization, fraudulent transfer and fraudulent conveyance, voidable preference, moratorium or other similar laws and related regulations or judicial doctrines from time to time in effect relating to or affecting creditors’ rights generally, and (ii) by general equitable principles and public policy considerations, whether such principles and considerations are considered in a proceeding at law or at equity.

Capital Southwest Corporation

December 15, 2017

Page 2

The opinion expressed herein is limited to the laws of the State of New York and the laws of the State of Texas, in each case as currently in effect, and we express no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as Exhibit (l)(2) to Post-Effective Amendment No. 2 to the Registration Statement on Form N-2 (Reg. No. 333-220385) (the “Registration Statement”), filed by CSWC to effect the registration of the Notes under the Securities Act of 1933 (the “Act”) and to the reference to Jones Day under the caption “Legal Matters” in the prospectus constituting a part of such Registration Statement. In giving such consent, we do not hereby admit that we are included in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day