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-methylheptane, and 3,-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,-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).