An inkjet printer that has an elongate array of nozzles for ejecting ink and ink conduits for supplying the array of nozzles with ink. The ink conduits are aligned with the longitudinal extent of the elongate array and have a plurality of pulse dampers individually in fluid communication with the ink conduits. Each pulse damper contains a volume of gas for compression by pressure pulses in the ink conduits, distributed along the length of the elongate array. A pressure pulse moving through an elongate printheads, such as a pagewidth printhead, can be damped at any point in the ink flow line. However, the pulse will cause nozzle flooding as it passes the nozzles in the printhead integrated circuit, regardless of whether it is subsequently dissipated at the damper. By incorporating a number of pulse dampers into the ink supply conduits immediately next to the nozzle array, any pressure spikes are damped at the site where they would otherwise cause detrimental flooding.