no thats the one you need to make the car run. That is the O2 sensor that the ECU uses to dial in the fuel trims.

O2 eliminator refers to either a downpipe that "eliminates" the 02 housing or the mod to eliminate the 2nd o2 sensor after the cat in cars running a test pipe (like me :D )

I'm about to go get a new O2 sensor from satan, its gonna cost me about 120 bucks :(

what exactly are the symptoms you are trying to get rid of to "make your car run well" ?

*edit* you are 4g63, right?