BTW, I just want to mention that all cleaning patches re NOT created equal! Some patches of a particular size are different thicknesses than others of the same size. They are also made out of different materials which have different properties. There are twill, 100% cotton, synthetic, single ply, heavy duty, etc.
In general I find Brownell's 100% cotton and 100% cotton twill to be some of the better ones. For 22's I actually use a single ply 100% cotton round patch rated for .270 caliber. I do not push the patch through the bore, I pull them through. I do push them through revolver cylinders (from the rear) and they work excellently. I also use Dewey Brass Loops and sand all of the rough edges and manufacturing marks off before using a new one.
Finding the proper type, brand and size of patch for each caliber is essential for proper and hassle free cleaning. Once I find the perfect patch, I buy them in bulk bags of 1,000 patches through Brownell's.