Repair Old Sub Floor

I recently added additional floor space to my exisiting kitchen. In the process several large and small holes were left in my old sub floor as I moved kitchen plumbing to the new addition. My question is, how do I best repair the holes in my subfloor so that I can lay either a laminate or hard wood floor over the holes?
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I normally add a piece of support plywood subfloor material between the joists with cleats attached to the joists to keep it in place, plus screws and some construction adhesive, then cut a patch of more plywood the same thickness as the original subfloor cut to fit into the opening, again screwed and glued down to the support plywood. This way your floor is flat and well supported.

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EXT wrote:

I normally remove all of the old subfloor, plywood isn't that expensive. I then do any insulating or other work while the space is accessible if it's a finished space below, then install new subflooring with plenty of construction adhesive to prevent any potential squeaks. The time you spend cutting and fitting patches eats up any savings in the cost of new plywood.
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