  The molecular ion H$_2^+$ is studied under strong confinement conditions
produced by a spherical barrier centered in the gravity center of the molecule.
Results for the potential curves are obtained by diffusion Monte Carlo methods
for the ground state (X$^2\Sigma_g^+$) and the first excited state
(A$^2\Sigma_u^+$), and reported as functions of the internuclear distance d for
different values of the confinement radius. Results show that the compressed
state corresponding to both $^2\Sigma_g^+$ and $^2\Sigma_u^+$ present deep
minima in their potential curves, due to the increased space for electron
wave-functions when the protons are displaced from the barrier surface.
