Accurate age–depth models are essential both for selecting suitable drill sites and for providing age constraints once the ice has been extracted. Such models rely on inverse ice flow methods constrained by dated radar internal reflecting horizons (IRHs) and on the parameterisation of several processes including the accumulation rate, the vertical velocity profile, and basal conditions. In particular, the treatment of basal processes, basal melting or stagnant ice, has an impact on the age of the deepest ice. Previous implementations parameterised basal conditions through a mechanical ice thickness, which truncated the shear layer in the melting regime, leading to an underestimation of basal melt rates and an overestimation of basal age. Here we introduce a dimensionless parameter ∆ that unifies the treatment of basal melting and stagnant ice, and we implement it in both a 1D and a 2.5D pseudo-steady-state inverse model. The 1D model was applied to three independent radar datasets covering the Dome C region. The 2.5D model was applied to an EDC–BELDC radar transect superimposed onto a flow line along which the Beyond EPICA Oldest Ice Core project aimed to retrieve a continuous ice core of up to 1.5 Ma from Little Dome C (LDC), Antarctica, referred to as the Beyond EPICA–Little Dome C (BELDC) ice core. The 2.5D model produces the bottom age of ∼800 ka for the EDC ice core which is in good agreement with measurements, confirming the validity of our methodology. The complete absence of accreted ice in the modelled particle trajectories is in contrast to the previous implementations. At the BELDC site, the model finds a 194 m thick layer of stagnant ice, consistent with the ∼200 m thick basal unit identified in radar surveys. The modelled maximum age for meaningful palaeoclimatic reconstructions is 1.17 Ma (age at which the age density reaches the 20 kyr m^−1 threshold). At the new Million Year Ice Core (MYIC) drill site at Dome C North, the 1D model predicts a maximum resolvable age of 2.07 Ma with an age density of 6.5 kyr m^−1 at 1.5 Ma, confirming the potential of this site for recovering ice over the full Mid-Pleistocene Transition (about 1.25 to 0.7 Ma). The framework presented here is general and can be applied to any region in Antarctica and Greenland where high-quality dated radar isochrones are available.