Originally posted by Nan:
...Do you guys think it would help if I put more "filling" behind the picture so it can't move as much?
As Cliff pointed out, the frame's contents need to be able to acclimate to ambient changes by expanding and contracting. So, making the frame package tighter might actually make the wrinkling worse.
I agree that hinging is probably your best strategy if you don't have a dry mount press. For a photo up to about 16x20, two 1" square hinges would be adequate. Place the hinges only on the back of the top edge as noted above, and make sure the tape covers no more than 1/4" of the paper, so that 3/4" goes onto the mount board.
You can hinge with a good quality clear tape. 3M #888 is strong polyester with a very good acrylic adhesive; among the best if you can find it. For economy jobs, Scotch Tape is not too bad, but avoid anything like masking tape.
I also agree about avoiding spray adhesives. Aside from the toxicity issues, that kind of mounting is likely to fail within a few years.
One point that I don't recall seeing above:
Are you sure these photos were perfectly flat when you framed them? Often, slight damage occurs from handling before framing -- such as lifting with one hand. That damage does not show when the photo is flat on a table, with no shadows and with light coming from all directions. But when the same photo hangs on the wall, light usually comes from one direction and casts shadows, which make wrinkles much more visible.