A power-assisted tissue-aspiration instrument employing a new and improved twin-cannula assembly. The twin-cannula assembly includes: an outer cannula mounted stationary to the front portion of a hand-supportable housing containing an inner cannula reciprocation mechanism, and an inner cannula having an open-end type aspiration aperture. The outer cannula has three groups of outer aspiration apertures about its distal portion. The open-end type aspiration opening of the inner cannula reciprocates back and forth to a mid position between the first group of aspiration apertures, and the third group of outer aspiration apertures, so that vacuum pressure is always delivered to at least 1/2 of one the outer aspiration aperture groups as the inner cannula is reciprocated back and forward within the outer cannula.