
<PAGE>
                                                                     EXHIBIT 1.1
 
           [LOGO]
 
                               November 30, 1998
 
TO THE STOCKHOLDERS OF CIRCON CORPORATION
 
Dear Stockholder:
 
    On November 21, 1998, Circon Corporation entered into an agreement with
Maxxim Medical, Inc. and its wholly owned subsidiary that provides for the
acquisition of Circon for a price of $15 per share in cash. Under the terms of
the proposed transaction, Maxxim's subsidiary has commenced a tender offer (the
"Tender Offer") for all outstanding shares of Circon Common Stock at $15 per
share. The Tender Offer is currently scheduled to expire at 5:00 p.m., New York
City time, on Thursday, January 5, 1999.
 
    Completion of the Tender Offer is conditioned, among other things, upon the
tender of at least a majority of the outstanding Circon shares. Following
successful completion of the Tender Offer, all Circon shares not tendered and
purchased in the Tender Offer will be converted into the right to receive $15
per share in cash pursuant to a merger of Circon with Maxxim's subsidiary.
 
    YOUR BOARD OF DIRECTORS HAS UNANIMOUSLY APPROVED THE TENDER OFFER AND THE
MERGER AND DETERMINED THAT THE TERMS OF THE TENDER OFFER AND THE MERGER ARE FAIR
TO, AND IN THE BEST INTERESTS OF, CIRCON STOCKHOLDERS. ACCORDINGLY, THE BOARD OF
DIRECTORS UNANIMOUSLY RECOMMENDS THAT THE STOCKHOLDERS ACCEPT THE TENDER OFFER
AND TENDER THEIR SHARES.
 
    The recommendation of the Board of Directors is described in the
Solicitation/Recommendation Statement on Schedule 14D-9 filed by Circon with the
Securities and Exchange Commission and enclosed with this letter. In arriving at
its recommendation, the Board of Directors gave careful consideration to a
number of factors, including the opinion of Bear, Stearns & Co. Inc., financial
advisors to Circon, a copy of which is attached as Annex A to the Schedule
14D-9. We urge you to read carefully the Schedule 14D-9 in its entirety to that
you will be more informed as to the Board's recommendation.
 
    Also accompanying this letter is a copy of the Offer to Purchase and related
materials, including a Letter of Transmittal for tendering your shares. These
documents set forth the terms and conditions of the Offer and provide
instructions as to how to tender your shares. We urge you to read each of the
enclosed materials carefully.
 
    On behalf of the Board of Directors,
 
                                          George A. Cloutier
                                          President and Chief Executive Officer
