We describe phase-dependent wavelength scaling of high-order-harmonic generation efficiency driven by ultrashort laser fields in the midinfrared. We employ both numerical solution of the time-dependent Schrodinger equation and the strong field approximation to analyze the fine-scale oscillations in the harmonic yield in the context of channel-closing effects. We show, by varying the carrier-envelope phase, that the amplitude of these oscillations depends strongly on the number of returning electron trajectories. Furthermore, the peak positions of the oscillations vary significantly as a function of the carrier-envelope phase. Owing to its practical applications, we also study the wavelength dependence of harmonic yield in the "single-cycle" limit, and observe a smooth variation in the wavelength scaling originating from the vanishing fine-scale oscillations.