When a free-falling liquid droplet is hit by a laser it experiences a strong ablation-driven pressure pulse. Here we study the resulting droplet deformation in the regime where the ablation pressure duration is short, i.e. comparable to the time scale on which pressure waves travel through the droplet. To this end, an acoustic analytic model for the pressure, pressure impulse and velocity fields inside the droplet is developed in the limit of small density fluctuations. This model is used to examine how the droplet deformation depends on the pressure pulse duration while the total momentum to the droplet is kept constant. Within the limits of this analytic model, we demonstrate that when the total momentum transferred to the droplet is small the droplet shape evolution is indistinguishable from an incompressible droplet deformation. However, when the momentum transfer is increased the droplet response is strongly affected by the pulse duration. In this later regime, compressed flow regimes alter the droplet shape evolution considerably.