Grand-canonical transition-matrix Monte Carlo is combined with configurational-bias and expanded ensemble Monte Carlo techniques to obtain saturated densities and vapor pressures of select n-alkanes. Surface tension values for butane, hexane, and octane are also computed via the finite-size scaling method of Binder. The exponential-6 model of Errington and Panagiotopoulos is used to describe the molecular interactions. The effect of the number of configurational-bias trial conformations on the efficiency of phase equilibra calculations is studied. We find that a broad range of trial conformation numbers give reasonable performance, with the optimal value increasing with decreasing temperature for a fixed chain length. Phase coexistence properties are in good agreement with literature values and are obtained with very reasonable computing resources. Similar to other recently developed n-alkane force fields, the exponential-6 model overestimates the surface tension relative to experimental values. Statistical uncertainties for coexistence properties obtained with the current approach are relatively small compared to existing methods.