An endoscope accessory, which comprises: a flexible elongated sheet, sized to envelop a flexible endoscope or echoendoscope shaft, having first and second faces (2, 3), a proximal end portion, a midportion, a distal end portion, and opposed longitudinal edge portions (7, 8) coacting to form a flexible overtube when said longitudinal edge portions (7, 8) overlap, said overtube having a distal endportion, a proximal endportion, and defining an external surface, an internal surface, and a central through passageway for receiving therewithin an endoscope or echoendoscope shaft; an inflatable band on the first face of said sheet, extending across entire width of the sheet at the distal end portion of the sheet, and forming an inflatable sealing band on the internal surface of the flexible overtube when the opposed longitudinal edge portions (7, 8) coact to form the flexible overtube; an inflatable pocket on the second face of the sheet, extending across the entire width of the sheet at the distal end portion of the sheet, and forming an inflatable positioning ring on the external surface of the flexible overtube when the opposed longitudinal edge portions (7, 8) are joined to form the flexible overtube; an inflation tube in communication with said pocket and provided with an inflation catheter; and a catheter carried by the sheet; the catheter having a free, independently positionable distal end portion that terminates in an inflatable occlusion balloon; wherein upon inflation of the occlusion balloon, the positioning ring, and the sealing band create a closed space within a body cavity that is fillable with air and water for improving an examination with the endoscope or the echoendoscope; characterized in that the inflatable positioning ring is asymmetric and wherein the inflatable asymmetric positioning ring and the inflatable sealing band are eccentric relative to the longitudinal axis of the over tube. a flexible elongated sheet, sized to envelop a flexible endoscope or echoendoscope shaft, having first and second faces (2, 3), a proximal end portion, a midportion, a distal end portion, and opposed longitudinal edge portions (7, 8) coacting to form a flexible overtube when said longitudinal edge portions (7, 8) overlap, said overtube having a distal endportion, a proximal endportion, and defining an external surface, an internal surface, and a central through passageway for receiving therewithin an endoscope or echoendoscope shaft; an inflatable band on the first face of said sheet, extending across entire width of the sheet at the distal end portion of the sheet, and forming an inflatable sealing band on the internal surface of the flexible overtube when the opposed longitudinal edge portions (7, 8) coact to form the flexible overtube; an inflatable pocket on the second face of the sheet, extending across the entire width of the sheet at the distal end portion of the sheet, and forming an inflatable positioning ring on the external surface of the flexible overtube when the opposed longitudinal edge portions (7, 8) are joined to form the flexible overtube; an inflation tube in communication with said pocket and provided with an inflation catheter; and a catheter carried by the sheet; the catheter having a free, independently positionable distal end portion that terminates in an inflatable occlusion balloon; wherein upon inflation of the occlusion balloon, the positioning ring, and the sealing band create a closed space within a body cavity that is fillable with air and water for improving an examination with the endoscope or the echoendoscope;