It is known that in the absence of distortion, the necessary sampling density for a multiband signal is given by its spectral occupancy. However, in general, the samples have to he acquired nonuniformly. There exist sampling patterns such that reconstruction is feasible even if the actual spectral support of the multiband signal is not known. If the samples are distorted, an increased sampling density may lead to a superior performance. In this paper, we consider the case of small distortion due to fine quantization of the samples, and we derive a necessary condition on the optimal sampling density.