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;                                
| |   
| | 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;                                                   
| |   
| | 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)) and internal control over financial reporting (as
      defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant
      and have:
| |   
| |    | a)                                                                                                                                                                                                                                                                                                                                                                
| |   
| |    | b)                                                                                                                                                                                                                                                                                                                                                                
| |   
| |    | c)                                                                                                                                                                                                                                                                                                                                                                
| |   
| |    | d)                                                                                                                                                                                                                                                                                                                                                                
| |   
| | 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):                                           
| |   
| |    | a)                                                                                                                                                                                                                                                                                                                                                                
| |   
| |    | b)                                                                                                                                                                                                                                                                                                                                                                

Date: May 5, 2006

| | /s/ Robert L.
      Bagby      
| | -------------------------------
| | Robert L. Bagby                
| | Chairman of the Board
      and
| | Chief Executive
      Officer  

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