Dempster set a Cubs franchise record Wednesday when he worked the ninth inning of Chicago's 5-4 win over Los Angeles for his 23rd consecutive save. He has converted all of his opportunities since blowing a lead and getting the win in an 8-4 victory over St. Louis last July 24. (Updated 4/20/2006) Analysis: The Cubs' right-hander also hasn't allowed a run since converting a save against the Cardinals on Aug. 14. He has worked 30 1/3 scoreless innings since then, allowing 16 hits and 10 walks while fanning 28.