  We find non-rational conformal field theories in two dimensions, which are
solvable due to their correlators being related to correlators of Liouville
theory. Their symmetry algebra consists of the dimension-two stress-energy
tensor, and two dimension-one fields. The theories come in a family with two
parameters: the central charge c and a complex number m. The special case m=0
corresponds to Liouville theory (plus two free bosons), and m=1 corresponds to
the H3+ model. In the case m=2 we show that the correlators obey third-order
differential equations, which are associated to a subsingular vector of the
symmetry algebra.
