This paper makes two contributions to the carbon-sequestration literature. The first is the development of a theoretical framework in which sequestration and permit trading are analyzed jointly in the context of a competitive fringe model. The second is a numerical analysis demonstrating the role market structure, or market power, might play in the determination of an equilibrium sequestration allocation and carbon price. We present three comparative-static cases, the first two of which assess the impact of relative changes in the cost structures of the dominant firm and competitive fringe. For these two cases we find that the equilibrium allocation of sequestration aligns with a higher carbon price when the competitive fringe experiences an increase in its marginal cost parameter. Conversely, the carbon price falls when the dominant firm experiences a decrease in its marginal cost parameter. In a third case we evaluate the impact of stricter regulation on the abatement decisions of the polluting firm. Our results demonstrate the importance of incorporating into empirical supply-side models demand-side information that is reflective of an underlying market structure.