The shear-lag parameter, beta, employed in various problems of shear-lag analysis of composites is an unknown parameter which, in certain cases, is impossible to define. In this paper, a new methodology is proposed for the definition and subsequent experimental measurement of beta for various single-fibre model composites. It is argued that, if beta is defined as a fitting parameter for the solution of the shear-lag differential equation, then it can effectively serve as a stress-transfer efficiency index. The dependence of beta upon the conditions prevailing at the fibre-matrix interface will be demonstrated by measuring beta as a function of the fibre sizing in a carbon-epoxy composite system.