  We discuss a finite rectangular well as a perturbation for the infinite one
with a depth $\lambda^2$ of the former as a perturbation parameter. In
particular we consider a behaviour of energy levels in the well as functions of
complex $\lambda$. It is found that all the levels of the same parity are
defined on infinitely sheeted Riemann surfaces which topological structures are
described in details. These structures differ considerably from those found in
models investigated earlier. It is shown that perturbation series for all the
levels converge what is in contrast with the known results of Bender and Wu.
The last property is shown to hold also for the finite rectangular well with
Dirac delta barier as a perturbation considered earlier by Ushveridze.
