We fitted all of the several hundred {\it RXTE} PCA spectra of the Crab individually to a simple power-law model; the total number of counts in the composite spectrum is $>10^9$. We then used the spectrum of residuals to derive a calibration tool, called {\tt pcacorr}, that we apply to large samples of spectra for GX~339--4, H1743--322, and XTE J1550--564. Application of the tool improved the quality of all the fits, and the improvement is dramatic for spectra with $\gtrsim10^7$ counts. The Crab residual spectrum is somewhat different for each of the five PCA detectors, but it was relatively stable over the course of the mission. We recommend that {\tt pcacorr} be routinely applied to spectra with $\gtrsim10^6$ counts and that one include a systematic error of 0.1\%, rather than the 0.5--1\% value that has customarily been used. We expect that application of the tool will result in an increase in sensitivity of the PCA to faint spectral features by up to an order of magnitude.