Compared to standard histogram techniques, the broad histogram method allows us to increase the efficiency of Monte Carlo simulations by a tremendous amount. This gain of efficiency is achieved by measuring simulation averages of particular system observables (different from those used in standard histogram techniques), while the algorithm of the simulation can be left unchanged. In this paper, the broad histogram method is reformulated in a more mathematical and precise way. Furthermore, the method is extended to estimate the density of states as a function of more than one parameter. A quantitative investigation of the gain of efficiency of Monte Carlo simulations is performed. For the broad histogram method, we find a gain of efficiency which amounts to orders of magnitude in comparison to the standard histogram method.