We study the hydrogen atom confined to a spherical box with impenetrable walls but, unlike earlier pedagogical articles on the subject, we assume that the nucleus also moves. We obtain the ground-state energy approximately by means of first-order perturbation theory and show that it is greater than that for the case in which the nucleus is clamped at the centre of the box. The present approach is valid for strong confinement and resembles the well-known treatment of the helium atom with clamped nucleus. (Contains 1 figure.)