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Yes it will sound much better with the second cat gone. That's what I did to my truck and it sounded bad a**. Just make sure you hang on to the cat just in case you should need to have it welded back on for some reason.

 

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Personally I would just leave it on there to simplify things, it shouldn't choke things down that much. Besides a little back pressure will help with the low end torque. When I ditched my 2nd I just torched it off and had a muffler shop weld in a piece of pipe

 

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