The probability that tsetse flies (Glossina spp.) cross a barrier of o
dour-baited targets is calculated for barriers of different widths and
target density, and for tsetse flies with varying natural rates of su
rvival, 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 s
pecies which has a 2% natural daily mortality and a further 2% mortali
ty 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 6
4 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 numbe
rs of targets in the barrier by 50%. These biological considerations a
nd the economic costs of different target barriers suggest that, for a
ll tsetse fly species, a safe and relatively inexpensive barrier is ac
hieved with barrier width 8d when the optimum target density is roughl
y the same as for normal operational areas. This has the important pra
ctical consequence that there is no need to treat barriers as a specia
l case. Practical results from research and control operations in Zimb
abwe are in accord with the theoretical findings, but further work is
required to ascertain whether the safety margin, and hence costs, can
be reduced.