We present the exact solution of a two-dimensional directed walk model of a
drop, or half vesicle, confined between two walls, and attached to one wall.
This model is also a generalisation of a polymer model of steric stabilisation
recently investigated. We explore the competition between a sticky potential on
the two walls and the effect of a pressure-like term in the system. We show
that a negative pressure ensures the drop/polymer is unaffected by confinement
when the walls are a macroscopic distance apart
