Deformation and failure mode of carbonate rocks depend on the confining pressure. In this study, the mechanical behavior of a limestone with an initial porosity of 14.7% is investigated at constant stress. At confining pressures below 55 MPa, dilatancy associated with microfracturing occurs during constant stress steps, ultimately leading to failure, similar to creep in other brittle media. At confining pressures higher than 55 MPa, depending on applied differential stress, inelastic compaction occurs, accommodated by crystal plasticity and characterized by constant ultrasonic wave velocities, or dilatancy resulting from nucleation and propagation of cracks due to local stress concentrations associated with dislocation pileups, ultimately causing failure. Strain rates during secondary creep preceding dilative brittle failure are sensitive to stress, while rates during compactive creep exhibit an insensitivity to stress indicative of the operation of crystal plasticity, in agreement with elastic wave velocity evolution and microstructural observations.