Thin compressive layers within a laminar ceramic arrest large cracks (surface and internal) and produce a threshold strength. This phenomenon increases the damage tolerance of ceramics and will allow engineers to design reliable ceramic components for structural applications. The stress intensity factor derived for a crack sandwiched between two compressive layers suggests that the threshold strength is proportional to the residual compressive stress and the thickness of the compressive layer and is inversely proportional to the distance between the compressive layers. Laminates composed of thick alumina layers (605 +/- 11 micrometers) and thin mullite/alumina compressive layers (37 +/- 1.4 micrometers) fabricated for this study had a threshold strength of 482 +/- 20 megapascals, in fair agreement with the theory.