CERTIFICATIONS

EXHIBIT 31(i)

I, Robert L. Bagby, certify that:

|1. |  | I have reviewed this annual report on Form 10-K of A.G. Edwards,
Inc.;
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|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;
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|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 and cash flows of
the registrant as of, and for, the periods presented in this report;
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|4. |  | The registrants other certifying officer and I are
responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the
registrant and have:
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|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 registrant, 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;
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|b) |  | Evaluated the effectiveness of the registrants disclosure
controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the end
of the period covered by this report based on such evaluation; and
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|c) |  | Disclosed in this report any change in the registrants
internal control over financial reporting that occurred during the registrants most recent fiscal quarter (the registrants fourth fiscal
quarter in the case of an annual report) that has materially affected, or is reasonably likely to materially affect, the registrants internal
control over financial reporting; and
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|5. |  | The registrants other certifying officer and I have
disclosed, based on our most recent evaluation of internal control over financial reporting, to the registrants auditors and the audit committee
of the registrants board of directors (or persons performing the equivalent functions):
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|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 registrants ability to
record, process, summarize and report financial information; and
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|b) |  | Any fraud, whether or not material, that involves management or
other employees who have a significant role in the registrants internal control over financial reporting.
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Date: May 13, 2004

| | /s/
Robert L. BagbyRobert L.
BagbyChairman of the Board andChief Executive Officer
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