We show that a rich variety of crystalline structures, and a corresponding diversity of the associated phase diagrams, result from the presence in the pair potential of a soft repulsion in addition to a hard core. We use different forms for the soft repulsion, and show that the results are sensitive to the details of the potentials (in particular, their convexity) even if the range of the soft repulsion is limited to a small fraction of the hard-core diameter. Our demonstration combines exact ground-state analysis with first-order perturbation theory at finite temperatures. The relevance of our work to certain features found in real systems is also discussed. (C) 2001 American Institute of Physics.