  X-ray and Sunyaev-Zeldovich effect observations can be combined to measure
the distance to clusters of galaxies. If the intracluster gas distribution is
not spherical, but elongated by a factor of Z along the line of sight, the
inferred distance is increased by Z, and H0 is decreased by the same factor.
Averaging the inferred value of H0 over a sufficiently large sample of clusters
can reduce any systematic bias due to cluster shapes, provided the clusters are
selected without any preferred orientation. Even so, elongation contributes
significantly to the variance in the measured distances and in the inferred
value of H0.
  With the addition of gravitational lensing observations, it is possible to
infer the three-dimensional shape of clusters, provided the gas is in
hydrostatic equilibrium. We demonstrate a specific method for finding the shape
and correcting the measured distances to individual clusters. To test this
method, we apply it to artificial observations of simple model clusters. We
recover the true distances to each of our clusters without detectable bias, and
with statistical errors due to measurement uncertainties of 4 to 6%.
