  Recent studies have shown that (a) quantum effects may be sufficient to
support a wormhole throat and (b) the total amount of "exotic matter" can be
made arbitrarily small. Unfortunately, using only small amounts of exotic
matter may result in a wormhole that flares out too slowly to be traversable in
a reasonable length of time. Combined with the Ford-Roman constraints, the
wormhole may also come close to having an event horizon at the throat. This
paper examines a model that overcomes these difficulties, while satisfying the
usual traversability conditions. This model also confirms that the total amount
of exotic matter can indeed be made arbitrarily small.
