leveling a floor


We removed tile and over 3/4 inch mud base and discovered the masterbath subfloor is about 3/4 inch out of level in 4 feet. We are not replacing the tile so we need to level the subfloor. We plan on pulling up the subfloor (some of it is water damaged) and sistering the joists with slightly higher joists as necessary to make the joists level. Seems like a better idea than shims which will probably crumble over time. My question is, do the sister joists which will be nailed to the real joists have to be full width or can we use 2 x 6 or 2 x 4's nailed to the 2x10 joists. What would be the best way to attach the sister joists? Any other suggestions on how to level a subfloor? Thanks.
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Art wrote:

Why not err on the side of caution and use the wider boards?
What would be the best

I think your idea is a good one. Nail it securely with construction adhesive to the sister. Clamp while nailing to secure board at desired height.
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Getting them in place may be difficult. We are working above a finished basement with a suspended ceiling. Tons of wires and plumbing to get around plus the suspended ceiling grid. Not to mention walls in the finished basement.
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Art wrote:

I personally would not hesitate to use long shims. Use construction glue, and they ain't goin' nowhere. What would crumble? Seems more sound than a 2x4 nailed to the side of a joist.
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