  We study long polymer chains in a poor solvent, confined to the space between
two parallel hard walls. The walls are energetically neutral and pose only a
geometric constraint which changes the properties of the coil-globule (or
"$\theta$-") transition. We find that the $\theta$ temperature increases
monotonically with the width $D$ between the walls, in contrast to recent
claims in the literature. Put in a wider context, the problem can be seen as a
dimensional cross over in a tricritical point of a $\phi^4$ model. We roughly
verify the main scaling properties expected for such a phenomenon, but we find
also somewhat unexpected very long transients before the asymptotic scaling
regions are reached. In particular, instead of the expected scaling $R\sim
N^{4/7}$ exactly at the ($D$-dependent) theta point we found that $R$ increases
less fast than $N^{1/2}$, even for extremely long chains.
