Try "spybot: search and destroy" This picks up things that ad aware doesn't, runs faster, and has some extra very useful settings like "immunize" where you can prevent your comp from even getting certain spyware stuff in the first place. Also PC mag rated spybot much higher and preferred over ad aware.
As for spy sweeper...never heard of it
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System Specs - Asus P4PE mobo, P4 2.53 GHz, 1024 MB DDR 333 PC 2700 ram, Sound Blaster Audigy 2 Platinum, 80 GB Maxtor Diamond Max Plus 9 7200 rpm HD, 160 GB Western Digital Caviar, Antec True Power 430 Watt PSU, Chieftec Dragon Case with Clear Side Panel, ATI Radeon 9800, Cendyne 48x16x48 CD-RW, LG 16x DVD-Burner, Hitachi 17" Gamer's LCD Monitor, Asus TV Tuner Card