Cr:forsterite laser-based frequency combs are useful for spectroscopic purposes in the near-IR wavelength region. However, self-referenced Cr:forsterite combs tend to exhibit wide carrier-envelope offset frequency (f0) linewidths, which result in broad comb teeth. This can be attributed to significant frequency noise across the comb's spectral bandwidth. We have stabilized a prism-based Cr:forsterite laser comb and observed narrowing of the f0 linewidth from ∼1.4 MHz down to ∼100 kHz by changing only the prism insertion, and to 23 kHz by inserting a knife edge into the intracavity beam while keeping the same prism insertion. The noise dynamics of the Cr:forsterite laser frequency comb are investigated with the goal of explaining this f0 narrowing phenomenon.