What is a good technique for binding a saddle stitch booklet with a hard-ish cover? I'm working on a small saddle stitched booklet. The concept involves a relatively hard-ish, see-through cover. The first time around I used 36 pages of 120gsm offset paper in a single booklet. I simply folded a sheet of polypropylene and sewed everything together. This way the finished product doesn't stay completely closed/flat.

Is there a way I could execute this that would result in a more elegant product; one that stays closed? I'm thinking something where I sew the pages together, then make and/or attach the harder cover somehow differently. How might I accomplish my goal?
When using 120 grams paper, it's best to use several signatures/booklets of 4 pages each. Then you can sew these together using a bookbinding technique (I like coptic binding - YouTube has great tutorials). 

If you don't want to use a different bookbinding technique, you can make your booklet flatter by folding all the folded pieces separately and making sure you have a sharp fold before putting everything together.