An ink pressure regulator for regulating a hydrostatic pressure of ink supplied to an inkjet printhead, said regulator comprising: 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 for bubbling air bubbles into the chamber, each air bubble comprising an air cavity trapped inside a film or a body of ink; and an air channel connecting the air inlet and the bubble outlet, wherein said bubble outlet is dimensioned to control a Laplace pressure of air bubbles drawn into said chamber as result of supplying ink to the printhead, thereby regulating a hydrostatic pressure of the ink.