Electron–phonon interaction in the Si(111)-supported rectangular 7 3 phases of In is investigatedwithin the density-functional theory and linear-response. For both single-layer and double-layer 7 3 structures, it is found that the phonon-induced scattering of electrons is almost exclusivelydetermined by vibrations of In atoms. It is shown that the strength of electron–phonon coupling at theFermi levell(EF) increases almost twofold upon adding the second In layer. One of the reasons is thatadditional low-frequency modes appear in the phonon spectrum, which favors a strong enhancement ofl(EF). The agreement of the calculated parameterl(EF) = 0.99 for a double-layer structure as well as thesuperconducting transition temperatureTc= 3.5 K with experimental estimates indicates that the discoveredsuperconducting phase is probably a double-layer rectangular 7 3 In structure on Si(111) with a cover-age of 2.4 ML. This conclusion is also supported by goodagreement between the calculated electron bandstructure and ARPES measurements.