  We present an analysis of the classic wormhole geometries based on conformal
Weyl gravity, rather than standard general relativity. The main characteristics
of the resulting traversable wormholes remain the same as in the seminal study
by Morris and Thorne, namely, that effective super-luminal motion is a viable
consequence of the metric. Improving on previous work on the subject, we show
that for particular choices of the shape and redshift functions the wormhole
metric in the context of conformal gravity does not violate the main energy
conditions at or near the wormhole throat. Some exotic matter might still be
needed at the junction between our solutions and flat spacetime, but we
demonstrate that the averaged null energy condition (as evaluated along radial
null geodesics) is satisfied for a particular set of wormhole geometries.
Therefore, if fourth-order conformal Weyl gravity is a correct extension of
general relativity, traversable wormholes might become a realistic solution for
interstellar travel.
