I investigate the optimal role of carbon sequestration for mitigation in the presence of a ceiling on atmospheric carbon concentration and consider aspects that have so far only been analyzed in the context of a damage function to measure the consequences of climate change for society. I assume extraction costs to be stock-dependent, replace the proportional decay description of the global carbon cycle by a two-box model, investigate the differences resulting from linear versus convex sequestration costs, and consider oceanic instead of geological carbon storage. Using a two-box model allows the non-renewable aspects of the global carbon cycle to be accounted for and implies that carbon emissions have to decline at the ceiling due to the ongoing saturation of the ocean with respect to anthropogenic carbon. Convex sequestration costs result in a continuous use of such a technology and allow the ceiling to be reached later than without sequestration, whereas linear sequestration costs result in a discontinuous use of such a technology and earlier reaching of the ceiling. Consequently, taking into the account the uncertainties in defining an appropriate ceiling, the policy recommendations with respect to carbon sequestration differ crucially according to the underlying assumptions of sequestration costs. Furthermore, the ocean might be a storage option for captured carbon, but even though its storage capacity is probably not scarce by itself, the ongoing saturation of the complete carbon cycle has to be taken into account.