Maybe you could also try using a crochet needle to bind off. Preferably one that is a size larger than the needles used for the project. I've found this keeps my stitches looser than struggling to pass the first stitch over the second.
Use the crochet needle exactly the same as a regular needle - In pattern (or however it tells you to bind off) knit first 2 stitches, hook that second stitch with the crochet hook and pull it through the first. Then knit another stitch and pull it through, etc. Easy.