After estimation of total lung volume (V_(lung)) with the Cavalieri method, which can easily be integrated into the sampling procedure, point-counting in a cascade-sampling design estimates all necessary subcomponent volumes (V_V) from which total volumes (V) can be derived by multiplication by the reference volume. For surface area (S), intersection counting is used accordingly. The number (N) is estimated by disector counting. Number-weighted mean volume (ν_N) is estimated either by local methods, e.g. the nucleator or rotator, or globally by V/N. The volume-weighted mean volume (ν_V) is estimated by point-sampled intercepts. If both the number-weighted and the volume-weighted mean volumes are known, information on the size distribution of particles can be derived, since ν_V = ν_N·(1+CV²_N(ν)), where CV is coefficient of variation and ν is mean volume. Arithmetic mean barrier thickness (τ) is estimated with a combination of point and intersection counting. S_S: surface fraction; par: parenchyma; nonpar: nonparenchyma; alvepi: alveolar epithelium; capendo: capillary endothelium; oed: oedema; alvoed: intra-alveolar oedema; sepoed: septal oedema; pbvoed: peribronchovascular oedema; bab: blood–air barrier; epi: epithelium; int: interstitium; endo: endothelium; alvsurf: intra-alveolar surfactant; lbl: lamellar body-like forms; tm: tubular myelin; mv: multilamellar vesicles; uv: unilamellar vesicles; lb: lamellar bodies; type II: type II cell.