We demonstrate theoretical conditions for highly-effcient degenerate four-wave mixing in triply-resonant (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interactions of light in arbitrary microcavities is expressed in terms of a set of coupling coefficients that we rigourously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal frequency $\omega_0-\Deltaω$ can, in the presence of a pump light at $\omega_0$, be converted with quantum-limited efficiency into an output shifted signa of frequency $\omega_0 + \Deltaω$, and we derive expressions for the critical input powers at which this occurs. We find that critical powers in the order of 10m$W$ assuming very conservative cavity parameters (modal volume $\sim 10$ cubic wavelengths and quality factors $\sim 1000$). The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we alo derive them from simple photon-counting "quantum" arguments. Finally, using a linear stability anaysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.