Magnetron reactive ion etching of the group III-nitride ternary alloys InxGa1-xN and InxAl1-xN was investigated in BCl3 plasmas and also in SF6/BCl3, H-2/BCl3, and Ar/BCl3 gas mixtures. Etch rates were determined as a function of cathode power density, flow rate, pressure, and gas composition. Etch rates were achieved that were four to six times greater than previously reported for these materials, and at low cathode bias voltages (<100 V). The addition of H-2 and Ar to concentrations of 60% in BCl3 increased In0.25Ga0.75N etch rates by 35% and 90%, respectively. Auger electron spectroscopy measurements on In0.75Al0.25N showed a reduction in the surface In/Al ratio upon etching, but essentially no change in the surface composition of etched In0.25Ga0.75N.