Despite years of investigation, the solid, quasi-permanent component of comets, the nucleus, remains largely a mystery. Its composition and thermal properties determine the evolution of the more familiar and often spectacular cometary features, the coma and the tail. Under some circumstances, the (≈200 K) nucleus may be obscured by a dust cloud of much higher temperature. It appears that the most appropriate technology for the investigation of the surface and subsurface layers of the nucleus is millimeter-wave sensing from an interplanetary spacecraft. Simple radiative transfer models, adapted from methods used for the interpretation of remote-sensing data on terrestrial ice and snow fields, are used to predict the millimeter-wave spectra of representative model nuclei. The spectra guide the choice of the minimum set of observing frequencies that is required. An instrument configuration driven by these requirements and guided by available technology and the constraints of a proposed NASA spacecraft, is then derived.