Clonal expansion of premalignant lesions is an important step in the progression to cancer. This process is commonly considered to be a consequence of sustaining a proliferative mutation. Here, we investigate whether the growth trajectory of clones can be better described by a model in which clone growth does not depend on a proliferative advantage. We developed a simple computer model of clonal expansion in an epithelium in which mutant clones can only colonize space left unoccupied by the death of adjacent normal stem cells. In this model, competition for space occurs along the frontier between mutant and normal territories, and both the shapes and the growth rates of lesions are governed by the differences between mutant and normal cells' replication or apoptosis rates. The behavior of this model of clonal expansion along a mutant clone's frontier, when apoptosis of both normal and mutant cells is included, matches the growth of UVB-induced p53-mutant clones in mouse dorsal epidermis better than a standard exponential growth model that does not include tissue architecture. The model predicts precancer cell mutation and death rates that agree with biological observations. These results support the hypothesis that clonal expansion of premalignant lesions can be driven by agents, such as ionizing or nonionizing radiation, that cause cell killing but do not directly stimulate cell replication.