Several strategies have been proposed for creating transgenic cultivars from which transgene escape to wild relatives would seem unlikely; for example, to impede escape through pollen, a transgene could be inserted into chloroplast DNA (cpDNA), which in many crops is rarely transmitted through pollen. None of these strategies would be failsafe; for example, the rate of cpDNA transmission through pollen may be low but non-zero in many crops. Here, we study how the probability distribution of escape time depends on the rates of pollen and seed flow from the crop to wild populations, the number and sizes of the wild populations, the selection coefficient for the transgene, and a leakage parameter characteristic of the strategy, for example, the rate of cpDNA transmission through pollen. We find that even with a leakage parameter as small as 103, the probability of escape within as few as 10 generations could be appreciable.