Zero-order average-Hamiltonian theory is used to extend the product-operator description of coherent spin-spin cross-polarization to the case of a spin-12 coupled to a general object, like a molecular rotor or a quantum oscillator. The object, which is not necessarily in a Boltzmann equilibrium state, is assumed to have no interaction with the lattice and no internal relaxation capacity. The Bloch-Wangsness-Redfield (BWR) theory for incoherent processes like spin-lattice relaxation does not apply for such an isolated spin-object pair. Nevertheless spectral density at the Larmor frequency, of key importance in BWR theory, also plays a central role in object-induced spin polarization. Spectral density in our theory is represented by quantum operators J(-) and J(+). If J(-) and J(+) do not commute, the spin-object coupling may cause spin polarization in an initially saturated spin system. This represents a coherent mechanism for spin cooling, which in specific cases may lead to enhanced spin polarization above the thermal equilibrium value. A master equation is derived for general spin-object cross-polarization, and applied to the case of a spin pair inside a uniaxial rotor, and a spin coupled to a microelectronic LC circuit. Copyright 2000 Academic Press.