  We find exactly solvable N=2-supersymmetric flows whose infrared fixed points
are the N=2 minimal models. The exact S-matrices and the Casimir energy (a
c-function) are determined along the entire renormalization group trajectory.
The c-function runs from c=3 (asymptotically) in the UV to the N=2 minimal
model values of the central charge in the IR, leading us to interpret these
theories as the Landau-Ginzburg models with superpotential $X^{k+2}$.
Consideration of the elliptic genus gives further support for this
interpretation. We also find an integrable model in this hierarchy which has
spontaneously-broken supersymmetry and superpotential $X$, and a series of
integrable models with (0,2) supersymmetry. The flows exhibit interesting
behavior in the UV, including a relation to the N=2 super sine-Gordon model. We
speculate about the relation between the kinetic term and the cigar
target-space metric.
