Forcing dense suspensions of non-cohesive particles through constrictions might result in a continuous flow, an intermittent one, or indefinite interruption of flow, i.e. a clog. While one of the most important (and obvious) controlling parameters in such a system is the neck-to-particle size ratio, the role of the liquid driving method is not so straightforward. On the one hand, widespread volume-controlled systems such as syringe pumps result in pressure and local liquid velocity increases upon eventual clogs. On the other hand, pressure-controlled systems result in a decrease of the flow through the constriction when a clog is formed. The root of the question therefore lies in the role of interparticle liquid flow and hydrodynamic forces on both the formation and stability of an arch blocking the particle transport through a constriction. In this work, we study experimentally a suspension of non-cohesive particles flowing through a constricted channel (with neck-to-particle size ratio $3.03\leq D/d\leq 5.26$ ) in an intermittent fashion, in which they are most sensitive to parametric changes. Due to the stochastic nature of the intermittency, we make use of statistical distributions of arrest times and of discharged particles, and surprisingly, we find that the transport of non-cohesive suspensions through constrictions actually follows a ‘slower is faster’ principle under pressure-controlled driving: low imposed pressures yield intermittent non-persistent clogs, while high imposed pressures result in longer-lasting clogs, eventually becoming everlasting, and thus reducing the net particle transport rate.