The Baade–Becker–Wesselink (BBW) method remains one of most often used tools to derive a full set of Cepheid astrophysical parameters. The surface brightness version of the BBW technique was preferentially used during the past few decades to calculate Cepheid radii and to improve period–luminosity–colour relations. Its implementation requires a priori knowledge of Cepheid reddening values. We propose a new version of the BBW technique, which allows one to independently determine the colour excess and the intrinsic colour of a radially pulsating star, in addition to its radius, luminosity and distance. The new technique is a generalization of the Balona light curve-modelling approach. The method also allows calibration of the function F(CI0) = BC(CI0) + 10 log [Teff (CI0)] for the class of pulsating stars considered. We apply this technique to a number of classical Cepheids with very accurate light and radial-velocity curves. The new technique can also be applied to other pulsating variables, e.g., RR Lyrae stars. We also discuss the possible dependence of the projection factor on the pulsation phase.