There is provided an ink pressure regulator for regulating a hydrostatic pressure of ink supplied to an inkjet printhead. The regulator comprises: an ink chamber having an ink outlet for fluid communication with the printhead via an ink line; an air inlet open to atmosphere; a bubble outlet positioned for bubbling air into ink contained in the chamber; and an air channel connecting the air inlet and the bubble outlet. The bubble outlet is dimensioned to control a Laplace pressure of air bubbles drawn into the ink as result of supplying ink to the printhead. Hence, the hydrostatic pressure of the ink is regulated.