I just remove the stem and run the cleaner down both halves. The only pipe I have that I can't get the pipecleaner all the way through the stem is a churchwarden, and i just keep churchwarden pipecleaners on hand for that pipe.
Some people have this notion that if they take the stem off that it wont fit back. I am not sure where this comes from, but after setting in a pipe lounge for a few years watching these big meat handed guys rip their stems out like a gorilla opening a banana, I don't criticize them as much. Some guys just don't have the gentle dexterity or fine motor skills to do most things. However, I have to wonder if they are using some cheap off brand pipecleaner, as most of mine will reach the bowl with some to spare.Frankly speaking, why would anyone want to leave the stem on the pipe when cleaning? Dragging a dirty pipe stem back through the pipe seems counterproductive.