I keep my scraps and use them for paper piecing or other small projects, so I don't feel like it's a waste. I actually prefer to do my corners that way. I think I get better results because the stretch on the bias is reduced that way.
If you have enough space, you can sew another seam about 3/8 from the first one, towards the outside corner and cut in between them. You'd end up with a bunch of small 1/2 square triangle blocks in addition to your other blocks. I got this idea from the pineapple quilt on Quiltville -
http://quiltville.com/pineappleblossom.shtml