If you don't mind a bit of extra work, you can get rid of the loose threads entirely. Tear the strips, it really does help, but make them wide enough so you can turn under the raw edges before you stitch the loops. I use strips between 2 and 2 1/2 inches wide. I try to work so that the slipknot ties where strips are joined end up underneath or hidden in the loops, and by turning in the raw edges as I go, the end result is very clean, neat and I like the way they look, made this way. So long as you keep the stitches snug and even, washing usually won't affect these, and they stay neat and tidy. It IS more effort, but like you, I don't care for that thready look :-). You can press under the raw edges first if you like but I find it very time consuming, so now I just fold them in as I go along.