We re-express current-algebra sum rules for pion-nucleus elastic-scattering amplitudes as off-mass-shell, finite-contour forward dispersion relations. Saturating these latter with narrow levels, both in the continua and in the bound-state spectra, we analyse all available data on the real parts of pion-nucleus scattering lengths. We find that a good description of these data requires introducing explicitly a shell-model picture of the nuclear ground states: indeed, most of the effects observed in light nuclei (up to and including the 2s-1d shell) are described by a very naive, spherical-harmonic-oscillator picture, save for the few-nucleon systems lighter than4He, which behave as loosely bound nucleon clusters (and for6Li, a loosely bound d-α cluster). An output of this analysis is the pion-nucleon sigma-term, which turns out smaller than, but still consistent with, the estimate by the Karlsruhe-Helsinki collaboration from pion-proton scattering amplitudes: this originates in a reduction in the pion decay constantfπ from the mass-shell toq2=0, needed to reproduce the isospin dependence in the data; the accord between the two estimates is recovered by extrapolating the πN amplitude inboth the variablest andq2 and imposing elastic unitary.