Soooo, what should we do with the old 'corrupt' download files?

Some of my 'corrupt' downloads resume, and some of those 'corrupt' acknowledge the presence of past downloaded Mbs for that file, while others seem as if starting from 0 Mbs all over again. All of these files are in my "incomplete" folder marked "corrupt" and I don't know what to do with them. My hard drive is pert near maxed out, should I delete these files and start over, or does this software restart, as it seems to do for some and not other 'corrupt' downloads?