The Monte Carlo technique of Ferrenberg and Swendsen [Phys. Rev. Lett. 61, 2635(1988] is improved by efficiently determining the tails of the Boltzmann distribution at the appropriate temperature. This is achieved by combining several distributions generated at different temperatures to form a composite distribution. The composite distribution leads to values of the specific heat and energy which are accurate over the entire temperature range of interest. Results illustrating these improvements are reported for the square two-dimensional Ising model.