In a superconductor electrons form pairs despite the Coulomb repulsion, as a result of an effective attractive interaction mediated by, for example, phonons. In the present paper DeGennes’ description of the dynamically screened Coulomb interaction is adopted for the effective interaction. This model is generalized by including the elastic response of the charge-compensating background and the BCS gap equation is solved for the resulting effective electron–electron interaction. It is demonstrated that the superconducting critical temperature becomes strongly enhanced when the material is tuned close to a structural instability.