There are two areas of deflection that need to be addressed: along the joists and in between the joists - BOTh must meet industry standards, or your installation is at high risk of failure. Any squeaks are a big red flag. The subflooring also must be well attached to the joists.
So, to define the joist deflection, you need to know the length of the unsupported span (this is often NOT the room size), the species of wood (it DOES make a difference), the width, height, and spacing of the joists. Then, the subfloor must be a minimum of 5/8" quality subflooring material - often you can't reach the minimum standards if it is old and has lots of holes in it - the spec is for new stuff, and most people want more than the minimum.
You need to determine if it is the joists deflecting, the subfloor deflecting, or loose ply to the joists. The use of screws to hold the subflooring down is good if you don't first glue it to the joists, but if you use construction adhesive to glue the subfloor, ring-shank nails usually work fine - once the adhesive sets, they're sort of redundent anyways.
If the joists are deficient, you could add a couple of support piers and a beam below. If the subflooring is deficient, it's much easier to fix if you tear out what you have and add a second layer. Note, a second layer of ply is REQUIRED, if you're planning a natural stone tile verses a ceramic one. To save on height, you could use something like Ditra from www.schluter.com - it's about 1/2 the thickness of cbu, but it will NOT compensate for an improper subfloor.