Algorithms are presented to improve the efficiency for the generation of  trial orientations and for the calculation of the Rosenbluth weight in a configurational-bias Monte Carlo (CBMC) simulation. These algorithms were tested for N p T and N V T simulations of n-octane, 3-ethyl- heptane, and 3,4-dimethylhexane at different temperatures and densities using a preliminary version of  the TraPPE united-atom representation for the CH₃, CH₂ and CH groups. It was found that for a system of 144 molecules these algorithms speed up  the calculation three times for n-octane and almost four times for 3,4-dimethylhexane, resulting in a decreased difference in simulation time between a branched molecule and a linear isomer. For larger systems the speedup is even greater. It is shown that the excluded volume of an atom is the dominant term for the selection of  a trial orientation, which leads to an improved CBMC algorithm called dual cutoff configurational-bias Monte Carlo (DC-CBMC).