Any spyware prog on it's own will miss lots of nasties (they detect a maximum of 60% in tests) so you're actually recommended to use more than one at a time (unlike antivirus progs : they'll clash if you use more than one).
Another option is to look at the "Processes" in Task Manager (hold Ctrl and Alt, then press "Delete").
First close down any progs that you don't need (less processes to check) and then enter the process names into this site
http://www.processlibrary.com/
which will tell you if any such process is a nasty or not.
If it IS nasty, again search google for "<nastyName> remove" which often takes you to a Symantec site offering a removal tool.
It's probably much easier to just let the antispyware do all of this hard work for you!!