  It is shown that in the two-exponential version of Liouville theory the
coefficients of the three-point functions of vertex operators can be determined
uniquely using the translational invariance of the path integral measure and
the self-consistency of the two-point functions. The result agrees with that
obtained using conformal bootstrap methods. Reflection symmetry and a
previously conjectured relationship between the dimensional parameters of the
theory and the overall scale are derived.
