Replacement Grip or Cushion wrap

avatar male m

So im changing my Lining racket overgrip yesterday when a friend of mine borrow it & i saw the grip somewhat messy. But then i saw the original grip are thorn apart inside.

So, based on you guys experience, what you do? Replace the original grip then overlap with overgrip or just use cushion wrap & put overgrip on it?

What are the pros & cons?