Segregation of impurities and alloying elements to voids produces a shell of different composition which significantly affects the mechanical interaction with point defects. This interaction determines the capture efficiency for interstitials and vacancies, and contains several contributions. Two contributions, namely the change of the relaxation energy of the point defect, and the interaction with coherency strains, have not previously been considered. The former arises when composition affects the local shear modulus, and the latter, when it causes a change in lattice parameter. Both contributions are added to two considered in previous works, the image interaction and the stress-induced interaction. The total mechanical interaction is evaluated for voids coated with a shell of material with properties different from those of the matrix, and an expression is derived for the capture efficiency. It is found that shells with a shear modulus only a few per cent larger than in the matrix make voids strongly biased against interstitials. This strong effect is due mainly to the change in relaxation energy rather than to the image interaction. Therefore, shells with diffuse or sharp interfaces are equally effective. However, shells with lower shear modulus are ineffective unless they possess a larger lattice parameter.