A new method is proposed that improves the performance of independent component analysis (ICA) algorithms for separating overlapping spectra under certain circumstances. The method is designed for Raman spectra in particular, although it should be applicable to spectra with similar line shapes, such as nuclear magnetic resonance. In the zero-noise case, conventional ICA fails to separate synthetic Raman spectra completely; by maximising smoothness, as opposed to other more traditional measures of statistical independence, better performance can be achieved. The new method is tested against artificial and real Raman spectra, and demonstrates improved performance for each. The algorithm is fully automated, requiring no user input or judgement in order to separate the spectra. Copyright © 2011 John Wiley & Sons, Ltd.