Delete First Option for Mirror Update?

We backup 5 files worth accounting files totaling about 900MB on a 1GB flash drive daily. Each day the oldest file is removed from the source and a new file is made. This creates a problem with a mirror update since the update occurs before the deletion of of the oldest file on the destination drive. This causes the update of the newest file not to occur but the deletion afterwards goes through. I believe there should be an option with a mirror update that the deletions are carried out first.