Perforated pulsation dampening devices of this invention comprise a housing having a structural wall section with opposed ends defining an internal chamber. The housing is characterized by a plurality of openings disposed therethrough. A compressible member is disposed within the internal chamber and positioned to be contacted by fluid passed from an outside surface of the housing through at least one of the openings. The compressible member is configured to absorb a known fluid flow variation or pressure pulsation in the fluid contacting the compressible member to attenuate the same. If desired, a sleeve can be interposed between an inside surface of the internal chamber and an outside surface of the compressible member.