Using the Box–Cox regression model with heteroscedasticity (BCHR), we re-examine the size distribution of the Portuguese manufacturing firms studied by Machado and Mata (2000) using the Box–Cox quantile regression (BCQR) method. We show that the BCHR model compares favourably against the BCQR method. In particular, the BCHR model can answer the key questions addressed by the BCQR method, with the advantage that the estimated quantile functions are monotonic. Furthermore, estimation of the BCHR model is straightforward and the confidence intervals of the BCHR regression quantiles are easy to compute. Copyright © 2006 John Wiley & Sons, Ltd.