An aspirator assembly for use during dental or medical procedures for removing body fluid and debris from the site of a procedure, comprising: an elongate tubular element (12, 122) defining a flow passage and having a connection end and a distal end; a soft and flexible cushioning aspirator tip, the flexible cushioning aspirator tip having a connection section establishing connection with said distal end of said elongate tubular element (12, 122) and being of sufficient thickness and resiliency to present a cushioned external surface for contact with the tissues of a patient, wherein an end opening of the elongate tubular element defines a receptacle within which the generally cylindrical connection section of the flexible cushioning aspirator tip is received, wherein the connection section includes one or more longitudinal relief grooves which, when the flexible cushioning aspirator tip is in assembly with the elongate tubular element, constitutes a vent or relief passage that ensures venting of excess adhesive when the tip is assembled to the tubular element; said flexible cushioning aspirator tip having a tubular tip head defining a rounded distal end portion and defining an aspiration chamber; said tip head defining a plurality of external longitudinal pressure relief channels extending along a major portion of said tubular tip head and terminating at said rounded distal end portion; and said flexible cushioning aspirator tip defining at least one fluid transfer opening within at least one of said plurality of external longitudinal pressure relief channels and permitting suction enhanced transfer of fluid therethrough and into said aspiration chamber and hence into said flow passage of said elongate tubular element (12, 122). an elongate tubular element (12, 122) defining a flow passage and having a connection end and a distal end; a soft and flexible cushioning aspirator tip, the flexible cushioning aspirator tip having a connection section establishing connection with said distal end of said elongate tubular element (12, 122) and being of sufficient thickness and resiliency to present a cushioned external surface for contact with the tissues of a patient, wherein an end opening of the elongate tubular element defines a receptacle within which the generally cylindrical connection section of the flexible cushioning aspirator tip is received, wherein the connection section includes one or more longitudinal relief grooves which, when the flexible cushioning aspirator tip is in assembly with the elongate tubular element, constitutes a vent or relief passage that ensures venting of excess adhesive when the tip is assembled to the tubular element; said flexible cushioning aspirator tip having a tubular tip head defining a rounded distal end portion and defining an aspiration chamber; said tip head defining a plurality of external longitudinal pressure relief channels extending along a major portion of said tubular tip head and terminating at said rounded distal end portion; and said flexible cushioning aspirator tip defining at least one fluid transfer opening within at least one of said plurality of external longitudinal pressure relief channels and permitting suction enhanced transfer of fluid therethrough and into said aspiration chamber and hence into said flow passage of said elongate tubular element (12, 122).