SAN FRANCISCO - One of Yahoo Inc.'s disgruntled shareholders is urging Microsoft Corp. (Nasdaq:MSFT) to make a more compelling case for its bid to buy the Internet pioneer's search operations -- a proposal that was trumped by an advertising deal Yahoo reached with Google Inc. (Nasdaq:GOOG)

Mithras Capital, which owns 1.7 million Yahoo shares (Nasdaq:YHOO), made the plea to Microsoft chief executive Steve Ballmer in a letter sent Thursday.

If Microsoft can more clearly explain why its alternative is more lucrative than the Google deal, Mithras believes a majority of Yahoo shareholders will support activist investor Carl Icahn's attempt to replace Yahoo's board at the Sunnyvale-based company's Aug. 1 annual meeting.

Icahn's board then could back out of the Google partnership and accept Microsoft's competing offer, wrote Mithras partner Mark Nelson. Mithras previously had thrown its support behind Icahn's slate of nine candidates.

Microsoft declined to comment on the Mithras letter.

The Redmond, Wash.-based software maker already has said it's still willing to consider a limited deal with Yahoo instead of buying the company in its entirety.

Microsoft offered to buy Yahoo for US$47.5 billion, or $33 per share, but withdrew the bid May 3 when Yahoo chief executive and co-founder Jerry Yang asked for $37 per share -- a price the shares haven't reached since January 2006.

Yahoo shares shed 18 cents Thursday to finish at $22.73.

Yahoo's handling of the Microsoft negotiations infuriated many shareholders, prompting Icahn to threaten a mutiny.

Icahn primarily wanted to oust Yahoo's board so he could revive sales talks with Microsoft. He hasn't elaborated on his strategy since Yahoo struck the deal with Google last week.

In an earlier letter to Yahoo's board, Icahn indicated he would consider a Google partnership if a deal with Microsoft couldn't be worked out.

Yahoo estimates Google's superior technology for showing ads alongside Internet search results will boost its annual revenue by about $800 million.

Microsoft said it offered to buy Yahoo's search business for $1 billion and invest another $8 billion in the remaining company at $35 per share. The deal also would have increased Yahoo's operating income about $1 billion annually, Microsoft estimated.

Yahoo is expecting the Google alliance to increase its annual cash flow by $250 million to $450 million.

"Microsoft claims that it has the superior transaction,'' Nelson wrote. "Now is the time...to substantiate the claim and take it directly to Yahoo shareholders.''