International relations scholarship overwhelmingly expects that relatively rising states will threaten and challenge declining great powers. In practice, however, rising states can also cooperate with and support declining powers. What explains the rising state's choice of policy? When do rising states support or prey on declining great powers, and why do such strategies vary across time and space? The answer depends on the rising state's broader strategic calculations. All things being equal, a rising state will generally support a declining power when the latter can be used to offset threats from other great powers that can harm the rising state's security. Conversely, when using a declining state to offset such challenges is not a plausible option, the rising state is likely to pursue a predation strategy. The level of assertiveness of support or predation, meanwhile, depends on the declining power's military posture: the stronger the declining state is militarily, the less assertive the rising state tends to be. A review of the strategies adopted by two relatively rising powers, the United States and the Soviet Union, toward a declining Great Britain after 1945, and of a rising United States vis-à-vis a declining Soviet Union in the late Cold War, illustrates how this argument outperforms explanations that focus instead on the importance of economic interdependence and ideology.