There are many good anti-spyware tools that are specialists in there field and there are many god free ones, I certainly wouldn't want to see avast dilute their expertise by adding anti-spyware; or become like one of the other bloated suites, that attempt to be Jack of all Trades, Master of None. I also don't like carrying all my eggs in one basket as an exploit on one element could effect/bypass everything.
My personal feeling is that you can chose the best in a class or certainly the one that suite you best, not what one providers thinks is best for you. This is feeling is often supported in the forums.
If you haven't already got this software (freeware), download, install, it provides good levels of protection, there are others.
1.
Ad-Aware2.
Spybot Search and Destroy3.
Spywareblaster Don't install this until you are clean.