A kinetically-constrained-model is studied numerically in two dimensions. Initially, as the system cools, the relaxation time follows a power-law divergence at a critical temperature, as in Mode-Coupling Theory (MCT). As cooling progresses further, dynamical arrest does not occur although the relaxation time starts to grow in an exponential fashion. This behavior is effectively captured by the Stochastic β-Relaxation (SBR) equations, which predict that the MCT’s dynamical arrest gives way to a crossover driven by fluctuations. A key and non-trivial prediction of the SBR framework is that below the critical temperature, the system’s dynamics is dominated by small, isolated compact regions that evolve much faster than the bulk of the system. A remarkable prediction is that the system’s slow-down is not due to the growth of these regions, but rather their decreasing prevalence with cooling. Furthermore the size of these regions shrinks as temperature decreases, implying a decrease of cooperativity. We numerically validate this scenario by means of a subtle analysis. In particular we have to reconcile the decrease of cooperativity with the numerical observation that the conventional dynamical correlation length grows monotonically upon supercooling. This misleading feature turns out to have a somewhat trivial origin caused by the facilitated nature of the dynamics and may explain similar observations in molecular dynamics simulations.