Some previous experiments and theory have suggested that the ultimate strengths of silicates are 1--2 GPa (10--20 kbar), that the ultimate strength of ice is about 0.1 GPa (1 kbar), and that the confining pressures of planetary interiors (~100 GPa) would not increase these strengths by more than a factor of two. Deviatoric stresses of these magnitudes are easily generated in planetary interiors by density heterogeneities of tens of kilometers radius. This implies that once such heterogeneities had formed, core segregation would not be further inhibited by the strength of a cold protoplanetary interior. It is further suggested that core segregation may be initiated by heterogeneous impact heating well before extensive near surface melting occurs, and that in the most favorable circumstance segregation could begin in a 700 km-radius protoplanet or a 500 km-radius icy satellite. These considerations increase the likelihood that core segregation in larger planets and satellites was essentially contemporaneous with accretion.