Hard flooring for small Loft

I would like to replace the carpet in the small 6' x 10' loft in my home office. I'd like to install some sort of allergy free surface, but my husband says that installing hardwood is problematic, because there is some give in the floor. Is there a non-carpet surface that I could install which would have a little give to it? This was a permitted project, so I imagine there isn't a lot of give.