A method of suppressing pressure oscillations in gas dispensed from a pressure-regulated vessel, the pressure-regulated vessel comprising: a pressure regulator assembly disposed in an interior volume thereof, the pressure regulator assembly comprising a first pressure regulator and a second pressure regulator, the second pressure regulator located downstream of the first pressure regulator and upstream of a valve head adapted for dispensing of fluid from the vessel, wherein the first pressure regulator has a set point pressure that is at least two times greater than a set point pressure of the second pressure regulator, the valve head comprising a discharge port, a flow control valve that is operable to control fluid dispensing, and an anti-pressure spike assembly adapted to combat pressure spiking in flow of fluid from said valve head at inception of fluid dispensing, wherein: the pressure regulator assembly comprises a flow control element that is openable and closable in response to pressure at the discharge port; the anti-pressure spike assembly includes a pressurization/depressurization assembly comprising a gas discharge line that is coupled to the discharge port of the valve head, a mass flow controller, and a cycling valve coupled to the gas discharge line that is selectively cyclable to establish fluid flow communication between the gas discharge line and one of a first branch line and a second branch line, the first branch line having a first flow isolation valve therein and coupled with a pump arranged to exert suction on the gas discharge line and to discharge gas via an exhaust line, the second branch line containing a pressurizing pump therein and joined to a pressurizing gas source, with a second isolation valve in such line serving to control flow of pressurized gas to the pressurizing pump, the method including repetitively and alternatingly applying pressure and reducing pressure at the discharge port of the vessel so that the flow control element of the pressure regulator assembly is cyclically opened and closed for a predetermined time period to stabilize pressure and suppress pressure oscillations in subsequent dispensing operation of the fluid supply package. the pressure regulator assembly comprises a flow control element that is openable and closable in response to pressure at the discharge port; the anti-pressure spike assembly includes a pressurization/depressurization assembly comprising a gas discharge line that is coupled to the discharge port of the valve head, a mass flow controller, and a cycling valve coupled to the gas discharge line that is selectively cyclable to establish fluid flow communication between the gas discharge line and one of a first branch line and a second branch line, the first branch line having a first flow isolation valve therein and coupled with a pump arranged to exert suction on the gas discharge line and to discharge gas via an exhaust line, the second branch line containing a pressurizing pump therein and joined to a pressurizing gas source, with a second isolation valve in such line serving to control flow of pressurized gas to the pressurizing pump, the method including repetitively and alternatingly applying pressure and reducing pressure at the discharge port of the vessel so that the flow control element of the pressure regulator assembly is cyclically opened and closed for a predetermined time period to stabilize pressure and suppress pressure oscillations in subsequent dispensing operation of the fluid supply package.