In bedded sedimentary or mechanically anisotropic rocks, joints often occur in laterally persistent, parallel sets with distinctive spacing attributes. Three of those attributes include a positively skewed distribution of joint spacings, a positive correlation between median spacing and mechanical layer thickness, and the tendency for rocks to appear saturated with joints and to show a ratio of layer thickness to median joint spacing near one. We identify total applied strain, mechanical interaction, joint propagation velocity, and flaws as key variables in the progressive jointing process, and we use a one-dimensional model of mechanically interacting joints to characterize the specific influence on joint spacing, of the number, sizes, and size distributions of flaws in rock. For a given flaw size distribution, the mode flaw size has no effect on spacing distribution shape, median spacing, or saturation. Layers with fewer flaws approach saturation more slowly and reach it with fewer joints and larger median joint spacing. The joint spacing distributions in these layers have variance and skewness that may be 1--3 orders of magnitude larger than in layers with greater numbers of flaws. Flaw size range affects the rate at which a jointing layer approaches saturation but not the number of joints at saturation. Resulting spacing distributions are similar, although narrow flaw size ranges tend to promote greater numbers of closely spaced joints. The skewness of a flaw size distribution affects the rate at which layers approach saturation, as well as the shape of the resulting joint spacing distribution at saturation. Negatively skewed flaw size distributions promote close joint spacing and create spacing distributions with greater variance and skewness.