We reformulate the adiabatic inflow–outflow solution (ADIOS) model for radiatively inefficient accretion flows, treating the inflow and outflow zones on an equal footing. For purely adiabatic flows (i.e. with no radiative losses), we show that the mass flux in each zone must satisfy with n= 1, in contrast to previous work in which 0 < n < 1 is a free parameter but in rough agreement with numerical simulations. We also demonstrate that the resulting two-zone ADIOS models are not dynamically self-consistent without the introduction of an energy source close in to the central regions of the flow; we identify this with the energy liberated by accretion. We explore the parameter space of non-radiative models and show that both powerful winds and gentle breezes are possible. When small radiative losses (with fixed efficiency) are included, any centrally injected energy flux is radiated away and the system reverts to a power-law behaviour with n≲ 1, where n falls in a small range determined by the fractional level of radiative losses. We also present an ADIOS model for hypercritical (super-Eddington) disc accretion, in which the radiative losses are closely related to the flow geometry. We suggest that hyperaccretion can lead to either winds or breezes.