A mathematical procedure is presented for the fast determination and removal of phase shifts, peak shifts, and peak width variations in spectral data sets. The method is applicable to any spectrum type (NMR, Raman, infrared, etc.) that contains spectrally isolated peaks. The procedure is illustrated on a series of simulated spectra and on a series of low signal-to-noise NMR spectra containing a single disturbed peak. Its value in multivariate calibration is demonstrated on a series of Raman spectra of the solution co-polymerisation of styrene and butyl acrylate in dioxane. The prediction of styrene and butyl acrylate conversions from the Raman spectra using partial least squares regression appears to be sensitive to peak shifts and, to a lesser extent, to peak width variations. It is shown that after removal of peak shifts and peak width variations the ability of partial least squares to predict styrene and butyl acrylate conversions is considerably improved.