CC, there is a way to connect the ends of your binding using a diagonal seam which eliminates all the bulk you are not lovin'. I doubt if I would be able to do it today if I hadn't been taught in person how to do it early on in my quilting journey. It involves placing the two ends together (RST) in the form of an L, then drawing a diagonal line and sewing on the line. You may have to scrunch the quilt up a lot under the needle. Then you trim the seam and press it open.
Yeah ... I'll see if I can find a tute on the web and post it. Once you learn it, you'll never use any other method.
OK, here's a tutorial on my favorite method for closing your binding. It has pictures and is easy to follow. Hope it helps!
http://www.squashhousequilts.com/201...-tutorial.html