As shown in the early 1960s, the gain in stimulated Raman scattering (SRS) is drastically suppressed when the rate of creation of phonons (via a pump-to-Stokes conversion) is exactly balanced by the rate of phonon annihilation (via a pump-to-anti-Stokes conversion). This occurs when the phonon coherence waves—synchronized vibrations of a large population of molecules—have identical propagation constants for both processes; i.e., they are phase-velocity matched. As recently demonstrated, hydrogen-filled photonic crystal fiber pumped in the vicinity of its zero-dispersion wavelength provides an ideal system for observing this effect. Here we report that Raman gain suppression is actually a universal feature of SRS in gas-filled hollow-core fibers and that it can strongly impair SRS even when the phase mismatch is high, particularly at high pump powers when it is normally assumed that nonlinear processes become more (not less) efficient. This counterintuitive result means that intermodal stimulated Raman scattering (for example, between LP01 and LP11 core modes) begins to dominate at high power levels. The results reported have important implications for fiber-based Raman shifters, amplifiers, or frequency combs, especially for operation in the ultraviolet, where the Raman gain is much higher