We investigate relations between spectral properties of a single-centre point-interaction Hamiltonian describing a particle confined to a bounded domain Ω ⊂ R d , d = 2, 3, with Dirichlet boundary, and the geometry of Ω. For this class of operators Krein's formula yields an explicit representation of the resolvent in terms of the integral kernel of the unperturbed one,`−∆ D Ω + z´− 1 . We use a moving plane analysis to characterize the behaviour of the ground-state energy of the Hamiltonian with respect to the point-interaction position and the shape of Ω, in particular, we establish some conditions showing how to place the interaction to optimize the principal eigenvalue.