Fragility index and cooperativity length characterizing the molecular mobility in the amorphous phase are for the first time calculated in drawn polylactide (PLA). The microstructure of the samples is investigated from wide-angle X-ray scattering (WAXS) whereas the amorphous phase dynamics are revealed from broadband dielectric spectroscopy (BDS) and temperature-modulated differential scanning calorimetry (TMDSC). The drawing processes induce the decrease of both cooperativity and fragility with the orientation of the macromolecules. Post-drawing annealing reveals an unusual absence of correlation between the evolutions of cooperativity length and fragility. The cooperativity length remains the same compared to the drawn sample while a huge increase of the fragility index is recorded. By splitting the fragility index in a volume contribution and an energetic contribution, it is revealed that the amorphous phase in annealed samples exhibits a high energetic parameter, even exceeding the amorphous matrix value. It is assumed that the relaxation process is driven in such a way that the volume hindrance caused by the thermomechanical constraint is compensated by the acceleration of segmental motions linked to the increase of degrees of freedom. This result should also contribute to the understanding of the constraint slackening in the amorphous phase during annealing of drawn PLA, which causes among others the decrease of its barrier properties.