We make the case for minimizing cavity length of extrinsic Fabry-Pérot (FP) cavities for use in fiber-tip sensors. Doing so mitigates multiple challenges that arise from using multimode fibers: mode averaging, phase uncertainty, amplitude reduction, and spectral modal noise. We explore these effects in detail using modal simulations, and construct pressure sensors based on this principle. We discuss the multimodal effects that we observe in our fiber sensors, and use simple filtering of the spectral signal to more easily measure pressure sensitivity. The concept of short-cavity FP interferometry is important for ensuring high quality and performance of multimode fiber sensors.