The constrained fraction of the amorphous phase of semi-crystalline polymers is in an out-of-equilibrium state so that "physical aging"-like features can be observed (e. g., by calorimetry) even above the glass transition temperature. This was already addressed in the literature in several semi-crystalline polymers at atmospheric pressure. Despite the well-known influence of pressure on molecular mobility, the pressure-sensitivity of these microstructure rearrangements has never been tackled. This study focuses on annealing in highly pressurized Poly-Ether-Ether-Ketone (PEEK), compared with atmospheric pressure. The phenomenon is tracked by ex-situ Differential Scanning Calorimetry (DSC). A significant influence of pressure is evidenced, without any complete equivalence with temperature. Indeed, pressure seems to confine rearrangements within spatially limited domains. The stability and coexistence of reorganization processes upon successive annealings is also investigated. Finally, relationships between constrained and free amorphous phase rearrangements are discussed via the different glass transition shifts observed after atmospheric or high pressure annealing. (C) 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 1148-1157, 2013