The deal was made Monday, just hours before the NHL trade deadline.
Desjardins had five goals and three assists in 58 games for San Jose this season. He also is used as a penalty killer. He is eligible to be an unrestricted free agent after the season.
Smith had five goals and four assists in 61 games. He is under contract for one more season.
The Sharks also acquired defenceman Karl Stollery from Colorado for forward Freddie Hamilton in a deal of minor leaguers.
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