Processing steps and tooling (FIGS. 5-7, 10-13 and 14-16) of the invention enable replacement of prior practice rivet button processes [FIGS. 3(a)-(d)] which progressively decreased unitary rivet button sheet metal thickness gauge so as to preclude use of thinner-gauge sheet metal (about 50 to 70 #/bb) rigid flat-rolled steel due to surface cracking (FIG. 4). Flat-rolled steel and rigid aluminum alloy sheet metal can be selected in new thickness gauges and preferred characteristics for container manufacture through use of the disclosed process [FIGS. 8(a)-(c)], which helps to achieve a major portion of desired rivet button height with only a minor decrease in starting thickness gauge [FIGS. 9(a) and (b)] to enable achieving desired final rivet button height with substantially uniform rivet button sheet metal thickness of greater than seventy-five percent of starting thickness gauge.