This work presents a new inclusive search for supersymmetry (SUSY) by the ATLAS experiment at the LHC in proton-proton collisions at a center-of-mass energy sqrt(s) = 7 TeV in final states with jets, missing transverse momentum and one or more isolated electrons and/or muons. The search is based on data from the full 2011 data-taking period, corresponding to an integrated luminosity of 4.7 inverse fb. Single- and multi-lepton channels are treated together in one analysis. An increase in sensitivity is obtained by simultaneously fitting the number of events in statistically independent signal regions, and the shapes of distributions within those regions. A dedicated signal region is introduced to be sensitive to decay cascades of SUSY particles with small mass differences ("compressed SUSY"). Background uncertainties are constrained by fitting to the jet multiplicity distribution in background control regions. Observations are consistent with Standard Model expectations, and limits are set or extended on a number of SUSY models.