From and after August 8, 1946, the royalty obligation to the United States under all leases requiring payment of royalty in excess of 12½ per centum, except leases issued or to be issued upon competitive bidding, is reduced to 12½ per centum in amount or value of production removed or sold from said leases as to (1) such leases, or such part of the lands subject thereto, and the deposits underlying the same, as are not believed to be within the productive limits of any oil or gas deposit, as such productive limits are found by the Secretary to exist on August 8, 1946, and (2) any production on a lease from an oil or gas deposit which was discovered after May 27, 1941, by a well or wells drilled within the boundaries of the lease, and which is determined by the Secretary to be a new deposit; and (3) any production on or allocated to a lease pursuant to an approved unit or cooperative agreement from an oil or gas deposit which was discovered after May 27, 1941, on land committed to such agreement, and which is determined by the Secretary to be a new deposit, where such lease was included in such agreement at the time of discovery, or was included in a duly executed and filed application for the approval of such agreement at the time of discovery.