Laboratory and numerical experiments show that when a chemically different layer overlies a hotter but otherwise denser layer, analogous to continental mantle lithosphere over asthenosphere, convective stability depends strongly on both the critical Rayleigh number and the buoyancy number, B, of the lithosphere-like layer. Sufficient cooling at low buoyancy number results in an oscillatory convective instability whereby the colder, more viscous, but chemically lighter layer is drawn into zones of downwelling flow adjacent to laterally extensive zones of upwelling. The critical Rayleigh number for instability increases with the buoyancy number from as little as ~30 for B = 0 to ~1000 for B ~ 0.5. Applied to continental lithosphere in a thermal and mechanical state near the instability threshold, this relationship implies that the lithospheric thickness must decrease as the mean density of the lithospheric mantle increases, consistent with the geological record.