A tissue removal system, comprising: a tissue removal device having a handpiece and an outer cannula extending distally from the handpiece, the outer cannula having a distal end, an outer cannula opening adjacent the distal end, and an outer cannula lumen; an inner cannula disposed in the outer cannula lumen and reciprocable within the outer cannula lumen, the inner cannula having an inner cannula lumen, a proximal end, an open distal end, a cutting edge at the distal end, a hinge, a cutting section, and a body section; and an elongated sleeve slidably disposed about the outer cannula, distal to a distal end of the handpiece, configured to be connected to a hub, wherein the sleeve includes an elongated sleeve channel section that comprises outer cannula channel being partially cylindrical and at least one supply channel being partially cylindrical or partially elliptic cylindrical and having an open distal end; wherein the outer cannula channel is positioned along a first channel axis and the outer cannula is received within the outer cannula channel, and the at least one supply channel is positioned adjacent the outer cannula channel so as not to be coaxial with the first channel axis, but positioned along a second channel-axis that is parallel to the first channel axis of the outer cannula channel throughout an entire length of the supply channel, wherein the supply channel and the outer cannula channel have the same length; wherein the open distal end of the supply channel serves as a fluid delivery conduit to a surgical site during operation of the tissue removal system; and wherein when the sleeve is removed from the outer cannula channel in an uninstalled condition, the at least one supply channel is in fluid communication with the outer cannula channel along the length of the sleeve. a tissue removal device having a handpiece and an outer cannula extending distally from the handpiece, the outer cannula having a distal end, an outer cannula opening adjacent the distal end, and an outer cannula lumen; an inner cannula disposed in the outer cannula lumen and reciprocable within the outer cannula lumen, the inner cannula having an inner cannula lumen, a proximal end, an open distal end, a cutting edge at the distal end, a hinge, a cutting section, and a body section; and an elongated sleeve slidably disposed about the outer cannula, distal to a distal end of the handpiece, configured to be connected to a hub, wherein the sleeve includes an elongated sleeve channel section that comprises outer cannula channel being partially cylindrical and at least one supply channel being partially cylindrical or partially elliptic cylindrical and having an open distal end; wherein the outer cannula channel is positioned along a first channel axis and the outer cannula is received within the outer cannula channel, and the at least one supply channel is positioned adjacent the outer cannula channel so as not to be coaxial with the first channel axis, but positioned along a second channel-axis that is parallel to the first channel axis of the outer cannula channel throughout an entire length of the supply channel, wherein the supply channel and the outer cannula channel have the same length; wherein the open distal end of the supply channel serves as a fluid delivery conduit to a surgical site during operation of the tissue removal system; and wherein when the sleeve is removed from the outer cannula channel in an uninstalled condition, the at least one supply channel is in fluid communication with the outer cannula channel along the length of the sleeve.