Removing >>groups<< of anchor points, w/o killing path?

I've got an auto-traced logo which looks good, but has 'wayyy too many points along straight edges. I'd like to clean it up.

As far as i can tell, there's no group equivalent to the POINT REMOVE tool (the 'minus' pen), that doesn't kill the path.

(Since these are straight lines, selecting and using "AVERAGE" actually works OK, but....)

Is there a group REMOVE function that will not kill the path? Tnx

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"Putting the HARM in 'harmonica' since 2005."
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Auto trace is just a plug-in. It usually results in a rough crappy result that needs to be cleaned up. I only use auto trace if I can't find a vector version of the logo. If you haven't already, I would suggest looking on a wonderful website called, Best Brands of The World.

http://www.brandsoftheworld.com

accounts are free and you need one to download. But all of the logos are Vector. I usually start there and if I can't find it then i turn to auto trace.

normally I try not to use the simplify path. because it cut so many corners. usually use the Delete Anchor point tool... which is under the Pen tool.