For shallow source depths, the moment-tensor elements with isotropic radiation patterns, Mzz and Mxx + Myy, are not resolvable in moment-tensor inversions of long-period surface-wave data because their respective Green's functions have similar frequency dependence. Examination of Green's functions at higher frequencies shows that, while resolution for some momenttensor elements improves, it is still not possible to resolve the isotropic-radiating moments from fundamental-mode data recorded at regional distances. On the other hand, the addition of higher mode Rayleigh-wave amplitudes can improve the resolution of these moments significantly, since there are appreciable differences between the higher mode Green's functions. An extension of Romanowicz's algorithm is presented to invert fundamental-mode and higher mode data for the second-order moment tensor. A source of “noise” in the estimation of the moment tensor for underground explosions is the spallation of geologic strata at ground zero, since this too can be a significant source of higher modes. The inversion proposed in this paper accounts for possible higher mode excitation due to spall using the source model of Day et al. The inversion is applied to regional recordings of the Harzer explosion of 6 June 1981 at the Nevada Test Site. The results of the inversion demonstrate a trade-off between the second-order moment tensor representation and the single, directed force used to represent spall. Observations and numerical simulations of spall provide estimates of spall source parameters, which in turn constrain the moment-tensor representation of Harzer. The results of this study demonstrate the clear need for observations to characterize the spall source associated with underground explosions. Furthermore, they demonstrate the potential benefit of using higher modes to refine estimates of the explosion moment with reduced uncertainties compared to moment determinations from fundamental-mode data alone.