A simple procedure for decoupling the vibrational modes in three-dimensional quantum calculations on triatomic molecule collisions is described. The technique is implemented in vibrational close-coupling, rotational infinite order sudden (VCC-IOS) calculations of vibrational excitation integral cross sections, rate coefficients and differential cross sections for the He+CO2 and He+SO2 collisional systems. By reducing the dimensionality of the integrals required to construct the vibrational close-coupling matrix elements, and by decreasing the size of the close-coupling basis set expansion, the decoupling method enables VCC-IOS calculations on these atom-triatom systems to be performed at higher energies than was possible previously. The decoupling technique might also make the extension of the VCC-IOS method to diatom-triatom and triatom-triatom collisions practicable.