Micro-fibre cloths (which you can often cadge from opticians free of charge) will do a better job. I think you can buy them in Woolworths and similar types of shops.
I've been told that another use for micro-fibre cloths is as a tack cloth; just dampen the cloth slightly, and use it as per a normal tack cloth. Apparently, it doesn't to raise the wood surface and has the advantage of being reusable. I've never tried this myself.
Gill