New trap designs for tsetse (Glossinidae), stable flies (Muscidae: Stomoxyinae), and horse flies (Tabanidae) were tested in Kenya to develop a multipurpose trap for biting flies. Many configurations and colour/fabric combinations were compared to a simplified, blue-black triangular trap to identify features of design and materials that result in equitable catches. New designs were tested against conventional traps, with a focus on Glossina pallidipes Austen and G. longipennis Corti, Stomoxys niger Macquart, and Atylotus agrestis (Wiedemann). A simple design based on minimal blue and black rectangular panels, for attraction and contrast, with a trap body consisting of an innovative configuration of netting, proved best. This 'Nzi' trap (Swahili for fly) caught as many or significantly more tsetse and biting flies than any conventional trap. The Nzi trap represents a major improvement for Stomoxyinae, including the cosmopolitan species S. calcitrans (Linnaeus), with up to eight times the catch for key African Stomoxys spp. relative to the best trap for this group (the Vavoua). Catches of many genera of Tabanidae, including species almost never caught in traps (Philoliche Wiedemann), are excellent, and are similar to those of larger traps designed for this purpose (the Canopy). Improvements in capturing biting flies were achieved without compromising efficiency for the savannah tsetse species G. pallidipes. Catches of fusca tsetse (G. longipennis and G. brevipalpis Newstead) were higher or were the same as catches in good traps for these species (NG2G, Siamese). Altogether, the objective of developing a simple, economical trap with harmonized efficiency was achieved.