Cavity theory is fundamental to understanding and predicting dosimeter response. Conventional cavity theories have been shown to be consistent with one another by deriving the electron (+positron) and photon fluence spectra with the FLURZnrc user-code (EGSnrc Monte-Carlo system) in large volumes under quasi-CPE for photon beams of 1 MeV and 10 MeV in three materials (water, aluminium and copper) and then using these fluence spectra to evaluate and then inter-compare the Bragg–Gray, Spencer–Attix and ‘large photon’ ‘cavity integrals’. The behaviour of the ‘Spencer–Attix dose’ (aka restricted cema), DS-A(Δ), in a 1-MeV photon field in water has been investigated for a wide range of values of the cavity-size parameter Δ: DS-A(Δ) decreases far below the Monte-Carlo dose (DMC) for Δ greater than ≈ 30 keV due to secondary electrons with starting energies below Δ not being ‘counted’. We show that for a quasi-scatter-free geometry (DS-A(Δ)/DMC) is closely equal to the proportion of energy transferred to Compton electrons with initial (kinetic) energies above Δ, derived from the Klein–Nishina (K–N) differential cross section. (DS-A(Δ)/DMC) can be used to estimate the maximum size of a detector behaving as a Bragg–Gray cavity in a photon-irradiated medium as a function of photon-beam quality (under quasi CPE) e.g. a typical air-filled ion chamber is ‘Bragg–Gray’ at (monoenergetic) beam energies ⩾260 keV. Finally, by varying the density of a silicon cavity (of 2.26 mm diameter and 2.0 mm thickness) in water, the response of different cavity ‘sizes’ was simulated; the Monte-Carlo-derived ratio Dw/DSi for 6 MV and 15 MV photons varied from very close to the Spencer–Attix value at ‘gas’ densities, agreed well with Burlin cavity theory as ρ increased, and approached large photon behaviour for ρ ≈ 10 g cm−3. The estimate of Δ for the Si cavity was improved by incorporating a Monte-Carlo-derived correction for electron ‘detours’. Excellent agreement was obtained between the Burlin ‘d’ factor for the Si cavity and DS-A(Δ)/DMC at different (detour-corrected) Δ, thereby suggesting a further application for the DS-A(Δ)/DMC ratio.