Using a simple model of ligand-receptor interactions, the interactions between ligands and receptors of varying complexities are studied and the probabilities of binding calculated. It is observed that as the systems become more complex the chance of observing a useful interaction for a randomly chosen ligand falls dramatically. The implications of this for the design of combinatorial libraries is explored. A large set of drug leads and optimized compounds is profiled using several different properties relevant to molecular recognition. The changes observed for these properties during the drug optimization phase support the hypothesis that less complex molecules are more common starting points for the discovery of drugs. An extreme example of the use of simple molecules for directed screening against thrombin is provided.