We use computational Bayesian methods to estimate parameters of a statistical model of gold, greenback, and real yield curves for US federal debt from 1791 to 1933. Posterior probability coverage intervals indicate more uncertainty about yields during periods in which data are especially sparse. We detect substantial discrepancies between our approximate yield curves and standard historical series on yields on US federal debt, especially during War of 1812 and Civil War surges in government expenditures that were accompanied by units of account ambiguities. We use our approximate yield curves to describe how long it took to achieve Alexander Hamilton’s goal of reducing default risk premia in US yields by building a reputation for servicing debts as promised. We infer that during the Civil War suspension of convertibility of greenback dollars into gold dollars, US creditors anticipated a rapid post war return to convertibility at par, but that after the war they anticipated a slower return.