We used Proraps for the newborn stage too, they seemed to fit better than the Thirsties, and they had the cut out for her cord. DD's didn't fall off until about 8 weeks. I do remember that the Proraps seemed to hold a urine smell after each change though, so I had to rotate them. But they were very affordable. At about 2 months, we switched to Thirsties and Swaddlebees.