The production, transport, and dissolution of carbonate shells plays an important role in the global carbon cycle. For instance, these processes affect the ocean's CO32- concentration, which, on glacial-interglacial timescales, is involved in the regulation of atmospheric pCO2. The saturation state of the ocean with respect to calcium carbonate suggests that any dissolution of calcium carbonate takes place not in the water column but at the seafloor. On the other hand, several authors suggest that a significant part of the dissolution takes place in the upper part of the water column. In the present paper, a simple model is presented to investigate under which circumstances dissolution of calcium carbonate in the water column may be plausible. Our analysis also includes dissolution facilitated by CO2 release from organic carbon remineralization, which may generate a microenvironment that is undersaturated with respect to CaCO3. In marine snow aggregates, however, respiration-driven dissolution is shown to be insignificant due to the size and settling velocities of the aggregates. With respect to aragonite, dissolution in the water column attributable to the bulk saturation state alone is significant and may well contribute to the alkalinity maximum in the undersaturated intermediate waters of the North Pacific Ocean. The suggested large loss of calcium carbonate dissolved in the water column (60--80% of CaCO3 production), however, cannot be explained by the mechanisms investigated here.