Yes, most of them have the same disease problems as larger roses (note that many "minis" have one or more of the roses in a larger class somewhere along the breed line). Some people just take a hedge clipper to them. I cut some off of the top, and then do more selective pruning. It is fairly easy to see which canes are the strongest, thickest. Those are the ones to use to measure against, and take out anything that is much thinner. Anything too thin won't support new growth in any case, and should be taken out. And always remove any canes that are diseased, damaged or dead.

Thanks for the reply, Diane. This is my first experience with a mini rose. The one I have is so full of tiny, thin canes and stems with loads of tiny leaves that are so crammed together. There are just a few thicker stronger canes. I guess it's never been pruned! It's blooming like crazy, though.