Many tuffs contain crystal, glass, and rock fragments that are supported by calcite cement, and some of these have recently been classified as carbonatites, i.e., igneous rocks dominated by magmatic carbonate minerals. In samples studied here, the cementing calcite has lower Sr and higher Mg concentrations, and higher 18O/16O but lower 13C/12C, than magmatic calcite. These chemical data, together with textural evidence, indicate that the cementing calcite in these tuffs was precipitated as coatings on the pyroclastic fragments by meteoric water. A single thin section of a calcite-cemented tuff (whether it holds carbonatite or silicate lapilli) can contain as many as five texturally and chemically distinct kinds of carbonate, precipitated sequentially, and never in equilibrium with each other. The secondary calcite in some occurrences may have formed by reaction of lime calcined by hot silicate magma from limestone wall rocks. Pyroclastic deposits that contain calcite only in pore-filling cement or replacing silicates should not be called carbonatites.