I actually didn't remove the the rear window, not all of it.The new window is glued to the old window with the vinyl adhesive and then the old window was cut out.
At least, that's what I SHOULD have done. I laid a piece of vinyl over the window and used a sharpie to mark where the lower edge was. Then, I cut along the line and glued the new vinyl to the old window. In order for this glue to make a good set you have to be sure and use sandpaper to rough up both the old and new vinyl. I let the glue dry, then measured and sharpie-ed around the rest of the window and cut it out. I then removed the old window using an exacto-knife, leaving about half an inch of vinyl all the way around. THIS WAS A MISTAKE! It turns out that the stock window is very tight and is pulling all the fabric together! When I removed the old window suddenly the new piece I cut out wasn't big enough anymore. I had to use the velcro along the top in order to make it long enough to reach. This is why it ended up bunching up so badly along the sides.
What I SHOULD have done:1. Leave old window in place.2. Lay new vinyl over old window.3. Sharpie the TOP of the new window to the old window and glue the TOP first (There's an overlapping piece of canvas that makes it hard to do the top last)4. Let top glue dry.5. Glue sides, making sure to leave enough new vinyl on the side to have something to pull on to leave no excess. It would help to have someone on the inside of the car to push outwards as you are pushing inwards to make sure the glue touches.6. Glue the bottom, again making sure to glue new vinyl to old vinyl and leave enough excess on the bottom to give your fingers something to grip onto and pull tight.7. Let all glue dry.8. Cut off excess new vinyl.9. From inside, CAREFULLY cut out old vinyl, making sure not to cut the new vinyl OR to cut off the old vinyl that the new vinyl is glued to.
At least, that's the procedure I THINK would work, given the mistakes I made.
At any rate, the new window is still a thousand times better than the old one, and after letting the glue cure overnight (like the bottle said) I was able to lower and raise the top without anything coming undone.