One of the key properties of biological molecules is that they can bind strongly to certain substrates yet interact only weakly with the very large number of other molecules that they encounter. Using a simple lattice model, we test several methods to design molecule-substrate binding specificity. We characterize the binding free energy and binding energy as a function of the size of the interacting units. Our simulations indicate that there exists a temperature window where specific binding is possible. Binding sites that have been designed to interact quite strongly with specific substrates are unlikely to bind nonspecifically to other substrates. In other words, the conflict between specific interactions between small numbers of biomolecules and weak, nonspecific interaction with the rest need not be a very serious design constraint.