We present an approach that improves the search for reliable astrophysical parameters (e.g. age, mass and distance) of differentially reddened, pre-main-sequence-rich star clusters. It involves simulating conditions related to the early-cluster phases, in particular the differential and foreground reddenings, and internal age spread. Given the loose constraints imposed by these factors, the derivation of parameters based only on photometry may be uncertain, especially for the poorly populated clusters. We consider a wide range of cluster (i) mass and (ii) age, and different values of (iii) distance modulus, (iv) differential and (v) foreground reddenings. Photometric errors and their relation with magnitude are also taken into account. We also investigate how the presence of unresolved binaries affect the derived parameters. For each set of (i)–(v) we build the corresponding model Hess diagram, and compute the root mean squared residual with respect to the observed Hess diagram. The parameters that produce the minimum residuals between model and observed Hess diagrams are searched by exploring the full parameter space of (i)–(v) by means of brute force, which may be time consuming but efficient. Control tests show that an adequate convergence is achieved allowing for solutions with residuals 10 per cent higher than the absolute minimum. Compared to a colour–magnitude diagram containing only single stars, the presence of 100 per cent of unresolved binaries has little effect on cluster age, foreground and differential reddenings; significant differences show up in the cluster mass and distance from the Sun. Our approach proves to be successful in minimizing the subjectiveness when deriving fundamental parameters of young star clusters.