Compressive layers placed within a laminate can arrest cracks. With increasing applied stress, the arrested crack can propagate through the compressive layer. These phenomena produce a material with threshold strength, i.e., failure cannot occur below a critical applied stress. A previously reported stress intensity function describes different variables, e.g., magnitude of compressive stress, thickness of compressive layer, and distance between compressive layers, which govern threshold strength. Laminar composites composed of thicker Al2O3 layers separated by thinner Al2O3/mullite layers were fabricated to test the different variables that are predicted to govern threshold strength. The data agreed well with the predicted values only when the magnitude of compressive stress and/or the thickness of the compressive layer were low. For these conditions, the crack extended straight through the compressive layers, as assumed by the model used to predict threshold strength. On the other hand, when the compressive stress and/or layer thickness were large, threshold strength was larger than the predicted value. In addition, for these conditions, the crack bifurcated through the compressive layer. The angle between the bifurcated cracks increased with increasing compressive stress.