CERTIFICATION PURSUANT TO SECTION 302 OF THE SARBANES-OXLEY ACT

I, Joseph C. Weller, certify that:

          1. I have  reviewed this report on Form N-CSR of RMK High Income Fund,
             Inc. (the "Fund");

          2. Based on my  knowledge,  this  report  does not  contain any untrue
             statement  of a  material  fact or omit to  state a  material  fact
             necessary   to  make  the   statements   made,   in  light  of  the
             circumstances under which such statements were made, not misleading
             with respect to the period covered by this report;

          3. Based  on  my  knowledge,  the  financial  statements,   and  other
             financial  information  included in this report,  fairly present in
             all  material   respects  the  financial   condition,   results  of
             operations, changes in net assets, and cash flows (if the financial
             statements  are  required to include a statement  of cash flows) of
             the Fund as of, and for, the periods presented in this report;

          4. The Fund's other  certifying  officer(s) and I are  responsible for
             establishing and maintaining disclosure controls and procedures (as
             defined in Rule 30a-3(c) under the Investment  Company Act of 1940)
             and internal  control over financial  reporting (as defined in Rule
             30a-3(d) under the Investment Company Act of 1940) for the Fund and
             have:

                  (a)  Designed  such  disclosure  controls and  procedures,  or
                  caused such disclosure  controls and procedures to be designed
                  under our  supervision,  to ensure that  material  information
                  relating to the Fund, including its consolidated subsidiaries,
                  is  made  known  to  us  by  others  within  those   entities,
                  particularly  during the period in which this  report is being
                  prepared;

                  (b) [Omitted];

                  (c)  Evaluated  the  effectiveness  of the  Fund's  disclosure
                  controls  and  procedures  and  presented  in this  report our
                  conclusions about the effectiveness of the disclosure controls
                  and  procedures,  as of a date  within  90 days  prior  to the
                  filing date of this report based on such evaluation; and

                  (d) Disclosed in this report any change in the Fund's internal
                  control over  financial  reporting  that  occurred  during the
                  second  fiscal  quarter of the period  covered by this  report
                  that has  materially  affected,  or is  reasonably  likely  to
                  materially  affect, the Fund's internal control over financial
                  reporting; and

          5. The Fund's other certifying  officer(s) and I have disclosed to the
             Fund's  auditors  and the audit  committee  of the Fund's  board of
             directors (or persons performing the equivalent functions):

                  (a) All significant  deficiencies  and material  weaknesses in
                  the design or  operation of internal  control  over  financial
                  reporting which are reasonably  likely to adversely affect the
                  Fund's  ability  to  record,  process,  summarize,  and report
                  financial information; and



                  (b)  Any  fraud,  whether  or  not  material,   that  involves
                  management or other  employees who have a significant  role in
                  the Fund's internal control over financial reporting.




Date:    December 2, 2004                     /s/ Joseph C. Weller
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                                                  Joseph C. Weller, Treasurer