  We consider semiclassical self-adjoint operators whose symbol, defined on a
two-dimensional symplectic manifold, reaches a non-degenerate minimum $b_0$ on
a closed curve. We derive a classical and quantum normal form which allows us,
in addition to the complete integrability of the system, to obtain eigenvalue
asymptotics in a window $(-\infty,b_0+\epsilon]$ for $\epsilon > 0$ independent
on the semiclassical parameter. These asymptotics are obtained in two
complementary settings: either a symmetry of the system under translation along
the curve, or a Morse hypothesis reminiscent of Helffer-Sj\"ostrand's
"miniwell" situation.
