  We consider self-avoiding polygons in a restricted geometry, namely an
infinite $L\times M$ tube in $\mathbb Z^3$. These polygons are subjected to a
force $f$, parallel to the infinite axis of the tube. When $f>0$ the force
stretches the polygons, while when $f<0$ the force is compressive. We obtain
and prove the asymptotic form of the free energy in both limits
$f\to\pm\infty$. We conjecture that the $f\to-\infty$ asymptote is the same as
the limiting free energy of "Hamiltonian" polygons, polygons which visit every
vertex in a $L\times M\times N$ box. We investigate such polygons, and in
particular use a transfer-matrix methodology to establish that the conjecture
is true for some small tube sizes
