A while ago I made a simple Buttercup bag from Rae Hoekstra's free pattern (here). I've used it heaps and love most things about it. Recently I needed to make two bags as gifts so took out the Buttercup pattern and added about 1 1/2" depth to it.
I added the depth to both the outer (lower) panel and the lining. It worked out fantastically and was the only change I needed to make.
Both bags are made from Essex linen/cotton. The grey bag is lined with a DSQuilts print while the tan bag has a Lecien print.