Many traditional Japanese komebukuro (rice bags) or kinchaku (drawstring bags) have a series of cord loops around the top, instead of having a drawstring channel. I have several antique bags in my collection with this kind of finish. These loops are very easy to make, but you do need a good strong cord to make the loops - a fine synthetic chainette or the 'Asian' cord sold for making decorative knotwork is ideal (now available from my online store).
The loops on the antique bag above seem to be knotted, but this is how I like to make them -
These are some of the fine cords I'm listing on the website today. The cords are polyester, very strong and won't break easily. The XL sashiko needle from Olympus is ideal for stitching these cords through the fabric. I also have thicker cords suitable for drawstrings. The perfect finishing touch for your Japanese style drawstring bag!