An extension of the spherical-head model (SHM) is developed to incorporate the elevation dependence observed in measured interaural time differences (ITDs). The model aims to address the inability of the SHM to capture this elevation dependence, thereby improving ITD estimation accuracy while retaining the simplicity of the SHM. To do so, the proposed model uses an elevation-dependent head radius that is individualized from anthropometry. Calculations of ITD for 12 listeners show that the proposed model is able to capture this elevation dependence and, for high frequencies and at large azimuths, yields a reduction in mean ITD error (averaged over the 12 listeners) of up to 47 microseconds (9% of the measured ITD value), compared to the SHM. For low-frequency ITDs, this reduction is up to 192 microseconds (27%). The values quoted in the abstract of the paper correspond to mean ITD error averaged over the 12 listeners and all available elevations.