The double levers seem to work in opposition to each other. After tightening one lever, the mount is not yet completely stable fore and aft until the second lever is actuated. I have owned a single lever mount, but never had it fitted to a rifle.
I was standing around in G&H's old shop in lower Broadway when a customer came in with a pre-War G&H Springfield with a single lever mount and a Lyman Alaskan scope. He wanted to change over to a 1" scope to replace the 22mm Alaskan. The gunsmith explained that the prewar scope mounts could not be changed over simply by changing the rings. The post-War rings would extend too far to the right and not be over the bore. He said that the only way of changing to a 1" setup was to change the whole mount, and operation which cost, I believe, $75.00 at that time.
While the customer was considering this proposition, I butted in with an offer to buy both old scope and mount for, I believe, $125.00, which the customer gladly accepted. I departed with the scope and top part of the mount in hand, and later received the base in the mail.
Later, while looking for a pre-War top part of a double lever G&H mount, I spied one lying on the desk of one of the owners of Dixie Gun Works, in Union City , Tennessee, I asked if it was for sale, and received a negative reply. I then offered to trade my single lever mount for it, and was accepted. It seems that his rifle had a single lever base and was missing the top part, just like mine was missing the double lever top part.