During joint propagation, the orientation of plume lines on joint faces allows for mapping the path taken by the crack tip line during rupture growth. Rupture shapes in layered, clastic sediments of the Devonian Catskill Delta (Finger Lakes district, New York) indicate joint growth through three stages, where velocity of the tip line, vtl, varies as a function of the crack-tip stress intensity, KI. The initial stage of growth is characterized by a rupture of approximately circular or elliptical shape that expands from an initiation flaw with a velocity, vtl. In some cases, primary growth involves self-correction, where an elliptical rupture redistributes the crack-tip stress so that the rupture returns to a more stable circular shape. The crack tip line eventually propagates to a bedding interface where properties of either a plastic or a noncohesive bedding interface cause vtl → 0 along a portion of the tip line. The onset of secondary growth occurs when the rupture tip line intersects both bedding interfaces and splits into two discontinuous segments that propagate synchronously as a single, coherent rupture. Nonuniform, nonsystematic vtl eventually interferes with the rupture's ability to grow coherently and thus leads to the transition to tertiary growth, characterized by the detachment of the coherent rupture into one or more independently propagating, noncoherent tip lines. Throughout all three stages of rupture growth, the KI-dependent vtl points to subcritical propagation. Variation from a smooth to rough plume morphology is consistent with propagation through region I of the subcritical regime with a transition at vtl≈10−5 m/sec. Rupture velocity may enter region II of the subcritical regime, but such a broad range of KI must be crossed to reach region III and quasistatic behavior at the critical stress intensity, KIc, that region II acts as a ‘barrier’ through which few joints pass, thus greatly limiting the number of postcritical joints in the Catskill Delta if not in the crust of the Earth.