The full-band Monte Carlo technique is currently the most accurate device simulation method, but its usefulness is limited because it is very CPU intensive. This work describes efficient algorithms in detail, which raise the efficiency of the full-band Monte Carlo method to a level where it becomes applicable in the device design process beyond exemplary simulations. The k-space is discretized with a nonuniform tetrahedral grid, which minimizes the discretization error of the linear energy interpolation and memory requirements. A consistent discretization of the inverse mass tensor is utilized to formulate efficient transport parameter estimators. Particle scattering is modeled in such a way that a very fast rejection technique can be used for the generation of the final state eliminating the main cause of the inefficiency of full-band Monte Carlo simulations. The developed full-band Monte Carlo simulator is highly efficient. For example, in conjunction with the nonself-consistent simulation technique CPU times of a few CPU minutes per bias point are achieved for substrate current calculations. Self-consistent calculations of the drain current of a 60nm-NMOSFET take about a few CPU hours demonstrating the feasibility of full-band Monte Carlo simulations.