Despite the abundant literature on obstacle crossing in humans, the question of how the central nervous system (CNS) controls postural stability during gait initiation with the goal to clear an obstacle remains unclear. Stabilizing features of gait initiation include anticipatory postural adjustments (APAs) and lateral swing foot placement. To answer the above question, 14 participants initiated gait as fast as possible in three conditions of obstacle height, three conditions of obstacle distance and one obstacle-free (control) condition. Each of these conditions was performed with two levels of temporal pressure: reaction-time (high-pressure) and self-initiated (low-pressure) movements. A mechanical model of the body falling laterally under the influence of gravity and submitted to an elastic restoring force is proposed to assess the effect of initial (foot-off) center-of-mass position and velocity (or “initial center-of-mass set”) on the stability at foot-contact. Results showed that the anticipatory peak of mediolateral (ML) center-of-pressure shift, the initial ML center-of-mass velocity and the duration of the swing phase, of gait initiation increased with obstacle height, but not with obstacle distance. These results suggest that ML APAs are scaled with swing duration in order to maintain an equivalent stability across experimental conditions. This statement is strengthened by the results obtained with the mechanical model, which showed how stability would be degraded if there was no adaptation of the initial center-of-mass set to swing duration. The anteroposterior (AP) component of APAs varied also according to obstacle height and distance, but in an opposite way to the ML component. Indeed, results showed that the anticipatory peak of backward center-of-pressure shift and the initial forward center-of-mass set decreased with obstacle height, probably in order to limit the risk to trip over the obstacle, while the forward center-of-mass velocity at foot-off increased with obstacle distance, allowing a further step to be taken. These effects of obstacle height and distance were globally similar under low and high-temporal pressure. Collectively, these findings imply that the CNS is able to predict the potential instability elicited by the obstacle clearance and that it scales the spatiotemporal parameters of APAs accordingly.