Pressure pulsation of an aircraft piston pump and accompanying vibrations are often sources of unreliability and fatigue of an aircraft hydraulic energy system. To reduce discharge pressure pulsation, a buffer bottle is usually installed inside the pump for space consideration that generally restricts its chamber volume resulting in a high working frequency range usually well exceeding the pressure pulsation frequencies corresponding to the normal operating speed range of the pump and hard to be adjusted once installed. To meet this challenge, this paper presents a method for designing a multi-element buffer bottle as an integrated fluid filter network formed by sub-elemental circuits (consisting of orifice, pipe and T-off) that can be assembled in an aircraft piston-pump. This design method of a compact fluid filter network is illustrated with a practical example based on a multi-element buffer bottle. Based on impedance models, results of an in-depth numerical investigation analyzing the effects of different buffer-bottle designs, geometrical parameters and adjustable orifice dimensions on pressure pulsation attenuation are discussed. The method for tuning the operating resonant frequency of a multi-element buffer bottle for pressure attenuation using a changeable orifice diameter is demonstrated experimentally confirming the buffer bottle as an attractive alternative to the conventional methods based on large-volume chambers.