In many problems of interest, solid objects are treated as rigid bodies in compressible flowfields. When these solid objects interact with certain features of the compressible flowfield, inaccurate solutions may develop. In particular, the well-known "overheating effect" occurs when a shock reflects off of a stationary solid wall boundary causing overshoots in temperature and density, while pressure and velocity remain constant (see, e.g., [3, 7, 13, 14]). This "overheating effect" is more dramatic when compressible flows are coupled to moving solid objects (e.g., moving pistons), where the nonphysical density and temperature overshoots can be cumulative and lead to negative values. We consider the general class of material interface problems where numerical methods can predict pressure and velocity adequately, but fail miserably in their prediction of density and temperature. Motivated by both total variation considerations and physical considerations, we have developed a simple but general boundary condition for this class of problems. This new boundary condition does not change the pressure or the velocity predicted by the numerical method, but does change the density and the temperature in a fashion consistent with the equation of state resulting in new values that minimize a specific measure of variation at the boundary. (C) 1999 Academic Press.