The 34,35Alβ decays were studied at the CERN on-line mass separator ISOLDE by β−γ,β−γ−γ and β−n−γ measurements, in order to corroborate thelow-level description of 34Si and to obtain the first information on the level structure of the N=21 isotope 35Si. Earlier observed γ lines in 34Al decay were confirmed and new gamma transitions following both beta decay and β-delayed neutron emission were established. The first level scheme in 35Si, including three excited states at 910, 974 and 2168 keV, is consistent with Jπ=3/2− and 3/2+ for the first two states respectively. Beta-decay half-life of T1/2=38.6(4) ms and beta-delayed neutron branching Pn value (Pn=41(13) were measured unambiguously. The significance of the single-particle energy determination at N=21, Z=14, for assessing the effective interaction in sd-fp shell-model calculations, is discussed and illustrated by predictions for different n-rich isotopes