  We study non-critical superstrings propagating in $d \le 6$ dimensional
Minkowski space or equivalently, superstrings propagating on the
two-dimensional Euclidean black hole tensored with d-dimensional Minkowski
space. We point out a subtlety in the construction of supersymmetric theories
in these backgrounds, and explain how this does not allow a consistent
geometric interpretation in terms of fields propagating on a cigar-like
spacetime. We explain the global symmetries of the various theories by using
their description as the near horizon geometry of wrapped NS5-brane
configurations. In the six-dimensional theory, we present a CFT description of
the four-dimensional moduli space and the global O(3) symmetry. The worldsheet
action invariant under this symmetry contains both the N=2 sine-Liouville
interaction and the cigar metric, thereby providing an example where the two
interactions are naturally present in the same worldsheet lagrangian already at
the non-dynamical level.
