We present a side-by-side comparison of the nonlinear behavior of four passive AlGaAs ridge waveguides where the bandgap energy of the core layers ranges from 1.60 to 1.79 eV. By engineering the bandgap to suppress two-photon absorption, minimizing the linear loss, and minimizing the mode area, we achieve efficient wavelength conversion in the C-band via partially degenerate four-wave mixing with a continuous-wave pump. The observed conversion efficiency [Idler(OUT)/Signal(IN)=-6.8 dB] is among the highest reported in passive semiconductor or glass waveguides.