The structural recovery of pressure-densified (PDG) and, for the first time, pressure-expanded (PEG) glasses are experimentally investigated using pressurizable dilatometry. Both glasses show early devitrification on heating, indicating that these glasses have more mobility, compared to the conventional isobarically formed glass. The Kovacs–Aklonis–Hutchinson–Ramos (KAHR) model of structural recovery is able to reasonably predict the behavior of the pressure-expanded glass, but the KAHR model fails with the pressure-densified glass. The results suggest two limitations of the model: (i) the structural recovery is assumed to depend on the instantaneous liquid state and (ii) the same relaxation kinetics are assumed for the temperature and pressure perturbations. Modification of the KAHR model, allowing the departure from equilibrium, δ, to initially depend on the liquid state that the glass came from and to evolve toward the state that the glass is going to, improves the ability of the model to predict the early devitrification for the pressure-densified glass. Another modification of the KAHR model, allowing the temperature and pressure perturbations to relax independently of one another, results in effectively capturing the increased thermal expansion coefficient of glass lines during heating, as well as a “memory”-like aging behavior, for the pressure-densified glass.