EXHIBIT 32.1

Certification Under Section 906 of the Sarbanes-Oxley Act of 2002

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each of the undersigned certifies that this periodic report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that information contained in this periodic report fairly presents, in all material respects, the financial condition and results of operations of Piper Jaffray Companies.

Dated: August 4, 2004

/s/ Andrew S. Duff  

Andrew S. Duff 

Chairman and Chief Executive Officer 

/s/ Sandra G. Sponem  

Sandra G. Sponem 

Chief Financial Officer