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Together with experimental data, theoretically predicted dipole moments represent a valuable tool for different branches in the chemical and physical sciences. With the diversity of levels of theory and basis sets available, a reliable combination must be carefully chosen in order to achieve accurate predictions. In a recent publication (arXiv:1709.05075 [physics.chem-ph]), Hait and Head-Gordon took a first step in this regard by providing recommendations on the best density functionals suitable for these purposes. However, no extensive study has been performed to provide recommendations on the basis set choice. Here, we shed some light into this matter by evaluating the performance of 38 general-purpose basis sets of single up to triple zeta-quality, when coupled with nine different levels of theory, in the computation of dipole moments. The calculations were performed on a data set with 114 small molecules containing second- and third-row elements. We based our analysis in regularised root mean square errors (regularised RMSE) as this procedure ensures relative errors for ionic species and absolute errors for species with small dipole moment values. Our results indicate that the best compromise between accuracy and computational efficiency is achieved by performing the computations with an augmented double zeta-quality basis set (i.e. aug-pc-1, aug-pcseg-1, aug-cc-pVDZ) together with a hybrid functional (e.g. wB97X-V, SOGGA11-X). Augmented triple-zeta basis sets could enhance the accuracy of the computations, but the computational cost of introducing such a basis set is substantial compared with the small improvement provided. These findings also highlight the crucial role that augmentation of the basis set with diffuse functions on both hydrogen and non-hydrogen atoms plays in the computation of dipole moments.