We present the theory of a scheme for frequency up-conversion from pump frequency omega(p) to a desired frequency omega(d) between 2 omega(p) and 3 omega(p). The proposed device consists of three nonlinear crystals in series inside a cavity resonating tight at a signal frequency omega(s). Sum-frequency generation (SFG) in the first crystal produces the desired radiation, omega(s) + omega(p) = omega(d). Second-harmonic generation (SHG) in the second crystal doubles the frequency of the residual pump, 2 omega(p) = omega(h), while the signal passes through unaffected, Optical parametric oscillation (OPO) in the third crystal generates the signal and idler frequencies, omega(h) = omega(s) + omega(i). A plane-wave analysis predicts a quantum efficiency close to 30% over an extended range of pump intensity. Iteration of the plane-wave solutions over many passes yields dynamics very similar to that recently calculated for the SFG-OPO device, As in that device, a small detuning of the SFG interaction enlarges the dynamic range yielding stable operation. Highest efficiency occurs when omega(i) is at the low-frequency end of the OPO crystal transmission window, As an example, we consider a device using a noncritically phase-matched KTP SFG crystal, a quartz crystal polarization rotator, an angle-tuned KTP SHG crystal, and a noncritically phase-matched LiNbO3 OPO crystal. This device is designed to convert lambda(p) = 1.064 mu m to lambda(d) = 0.455 mu m. We calculate a power conversion efficiency as great as 73%.