An inkjet printer comprises: (a) an inkjet printhead having an inlet channel and an outlet channel; (b) an ink reservoir; (c) an ink pressure regulator for regulating a hydrostatic pressure of ink supplied to the printhead; (d) a first ink line connecting the ink outlet and the inlet channel of the printhead; and (e) a second ink line connecting the outlet channel of the printhead and a return inlet of said ink reservoir, such that ink is supplied in a recirculating circuit. The ink pressure regulator comprises: an ink chamber having an ink outlet; an air inlet open to atmosphere; and an air channel connected to the air inlet. The air channel has a constriction defining a bubble outlet, which is configured as a slot. A width dimension of the slot is dimensioned to control a Laplace pressure of air bubbles drawn into the ink as result of supplying ink to the printhead, and thereby regulates a hydrostatic pressure of the ink.