Continuum percolation thresholds for fracture systems are based on models with random fracture locations, resulting in uniformly clustered systems in which all connections are fracture intersections. Fractures in natural systems can be either clustered or anticlustered, and a significant portion of the connectivity is achieved through fracture abutments or splays. Analytical and numerical methods are combined to define critical properties of isotropic networks of constant length lines as a function of fracture clustering and of the ratio of abutments to intersections. A second suite of numerical results indicates that the influence of these parameters varies as a function of the fracture length distribution. A preliminary predictor of critical density of anisotropic nonrandom systems with lognormal length distributions is derived and applied to a suite of natural fracture systems. Predicted connectivities are closer to the observed connectivities when the predictor is used than when connectivity is estimated from the random threshold.