After bending a mainspring barrel cover and ruining it I found a better way. I now use an inexpensive watch case press that I purchased from Harbor Freight (item# 91621) for about $15.00. It came with a set of nylon dies including two flat dies. After placing the body of the barrel on the lower die and carefully lining the cover up in the correct position, I can just snap the two parts together. It does a perfect job and does not distort the cover.
David