Best Glide Aviation Supply imports both types of BCB saws:
with rings and
with web loops. My saw is the ring type but long ago I removed the rings and replaced them with finger loops made from 550 cord. When I cut those 3"-4" logs, I only had my middle finger in the loop and it was quite comfortable (although I was wearing leather work gloves). If you like you can put small sticks thru the little 550 loops to form handles. Having small 550 loops only big enough for a gloved finger or a stick minimizes the bulk of the overall package.