Restricted class of traversable wormholes with traceless matter

Spherically symmetric, static traversable wormholes with traceless matter are obtained by solving the tracelessness constraint for a physical but specific choice of the redshift function. Both Morris-Thorne-type and Visser-type geometries are discussed with emphasis on the matter stress energy. In the former case the region over which matter violates the WEC can be made very small provided one does not demand a significant ``flare out'' from the throat. The latter (Visser-type) geometries have an exotic surface stress energy. Finally an analysis of traversability leads to interesting lower bounds on the throat radius of these wormholes.