Like Scott, I have a couple pipes with a very tight bend, so the pipe cleaner won't insert fully from the mouthpiece. I also clean from the other end (tenon end).
Twisting is a major help too.
Also sometimes I will pre-bend my cleaners to resemble the stem's curvature more before inserting. This helps some too.
I have noticed many pipe cleaners often have a slight curl or bur at one end, and this can make them very difficult to push through. I will, of course, use the other end.
If a cleaner is dropping fluff in your pipe, I would think to stop using those cleaners (duh) and get some other (read better) cleaners and ram the fluff outta your pipe. :lol: