The probablity that tsetse flies (Glossina spp.) cross a barrier of odour-baited targets is calculated for barriers of different widths and target density, and for tsetse flies with varying natural rates of survival, daily step lengths (d) and probabilities of being killed by an odour-baited target. If the barrier is only as wide as d, and for a species which has a 2% natural daily mortality and a further 2% mortality due to each target per unit area, tsetse flies have probability (P) of ca. 0.1 of penetrating the barrier even if the target density is 64 per unit area. To ensure that P < 0.001 the barrier must be about 4d wide for target densities 32 per unit area; doubling the width to 8d means that target densities could be cut by about 75%, and total numbers of targets in the barrier by 50%. These biological considerations and the economic costs of different target barriers suggest that, for all tsetse fly species, a safe and relatively inexpensive barrier is achieved with barrier width 8d when the optimum target density is roughly the same as for normal operational areas. This has the important practical consequence that there is no need to treat barriers as a special case. Practical results from research and control operations in Zimbabwe are in accord with the theoretical findings, but further work is required to ascertain whether the safety margin, and hence costs, can be reduced.