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Forcing dense suspensions of non-cohesive particles through constrictions might either 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 obvious. On the one hand, wide-spread volume-controlled systems 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 developed. The root of the question therefore lies on 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 experimentally analyse a suspension of non-cohesive particles in channels undergoing intermittent regimes, in which they are most sensitive to parametric changes. By exploring the statistical distribution of arrest times and of discharged particles, we surprisingly find that the transport of non-cohesive suspensions through constrictions actually follows a "slower is faster" principle under certain conditions.