Will carpeting the hardwood help with soundproofing?

Hi, I live in a lower flat and rent out my upper flat. When I moved in, the unit was empty, and likewise, I had no idea how loud the upper unit noise would be. The worst is the squeaking under the wood floors...it is a little better in the carpeting areas, but not too much better. That said, I previously refinished two of the main rooms with beautiful hardwood. It has helped me to attract nice tenants and I imagine it will help with resale. Still, any time I am between tenants I think about carpeting it (like now) as the noise is truly unbearable. However, now that I am at that point, I worry about doing it as in the long run, it may not help too too much. So, is there anything else I can do? I thought of perhaps having the boards tightened (re-nailed down) but it has been hard to find someone to do that. Then, if so, I could require area rugs in the wood areas. Thoughts, ideas, is there a better way to go?