The electronic and ionic response of a small metal particle in a static electric field is studied within the jellium model in which the ionic jellium background is assumed to be elastically deformable. Results of the calculation indicate that while the polarizability of the particle remains remarkably constant as the jellium stiffness is relaxed from perfect rigidity, there are nevertheless significant departures from the rigid jellium model in both the ionic and/or electronic makeup of the polarizability and the associated charge-density modulations. In particular, for Na clusters of up to 92 atoms the ionic component is shown to account for \ensuremath{\sim}10--15 % of the total polarizability. Numerically evaluated charge-modulation profiles, together with the variation of ionic polarizability with elastic stiffness, are presented and discussed.