Giant E₁ resonances in ⁴⁰Ca,⁴⁸Ca and ²⁰⁸Pb are calculated within a microscopic model which takes into account the 1p1h and 1p1h⊗phonon configurations and uses the same set of effective interaction parameters for all nuclei and phonons. The 2p2h correlations in the ground state, which are additional to those included in the RPA, are taken into account. It is shown that allowing for complex configurations noticeably improves the agreement with experiment as compared with the RPA mainly for the mean energies of the resonances in ⁴⁸Ca and ²⁰⁸Pb.