Two sets of thrust compactive shear bands and one set of dip-slip compactive shear bands with, in places, associated slip surfaces have been recognized for the first time in a peculiar high-porosity grainstones of the Calcare Massiccio Fm., a Lower Jurassic platform limestone deformed during the development of the late Messinian Cingoli anticline of northern Apennines, Italy. The deformation bands have been studied by field mapping, thin section image analysis, back scatter SEM imaging, and pressure pulse decay minipermeametry. The deformation micro-mechanism in the compactive shear bands is controlled by plastic smearing and grain size reduction of soft micrite peloids with rare grain crushing and even rarer pressure solution. Plastic smearing is characteristic of the micrite peloids and is different from mechanisms occurring in other known carbonate deformation bands where the grains are bioclastic fragments and sparite ooids. The syntectonic diagenetic episode that brought to cement precipitation in the high-porosity grainstones of the Calcare Massiccio caused the loss of porosity and a change in deformation style from strain localization accommodated by banding to classical faulting along slip surfaces accompanied by thick zones of gouge and breccia. The permeability reduction from the host rock normal to the slip surfaces with associated compactive shear bands is, on average, an order of magnitude, which is less than what measured across deformation bands in other porous carbonates. We speculate that the diagenetic history provides a conceivable hypothesis to explain the high porosity in a Mesozoic platform carbonate at the time of orogenic compression (late Messinian), so that deformation bands, hitherto unknown in this type of rock, could develop.