Filling voids in the case can be a help. I use felt fabric or rubber "waffle" material such as sold for drawer liners. Wherever possible I cut flat layers to fit, then for taller cavities I cut rectangles of fabric which I roll into cylinders to fit each hollow as closely as possible. These will compress, of course, so you can get nearly complete fill if you try.
A mat under the keyboard is essential. The best but most expensive and difficult to get is sorbothane, the cheapest and easiest is a folded towel.