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Independent evolution of similar traits in lineages inhabiting similar environments (convergent or repeated evolution) is often taken as evidence for adaptation by natural selection, and used to illustrate the predictability of evolution. Yet convergence is rarely perfect for two reasons. First, environments may not be as similar as they appear. Second, responses to selection are contingent upon available genetic variation and independent lineages may differ in the alleles, genetic backgrounds, and even the developmental mechanisms responsible for the phenotypes in question. Both impediments to convergence are predicted to increase as the length of time separating two lineages increases, making it difficult to discern their relative importance. We quantified environmental similarity and the extent of convergence to show how habitat and divergence time each contribute to observed patterns of morphological evolution in 212 species of stick and leaf insects (order Phasmatodea). Dozens of phasmid lineages independently colonized similar habitats, repeatedly evolving in parallel directions on a 23-trait morphospace, though the magnitude and direction of these shifts varied. Lineages converging toward more similar environments ended up closer on the morphospace, as did closely related lineages, and closely related lineages followed more parallel evolutionary trajectories to arrive there than more distantly related ones. Remarkably, after accounting for habitat similarity, we show that divergence time reduced the extent of convergence at a constant rate across more than 100 My of separation, suggesting even the magnitude of contingency can be predictable, given sufficient spans of time.