A system for removing obstructive material from a body lumen, comprising: an elongate tubular member comprising a proximal end, a distal end sized for introduction into a body lumen, a lumen extending between the proximal and distal ends, and an annular expandable member on the distal end that is expandable from a collapsed configuration to an expanded configuration wherein the expandable member adopts a tapered shape that flares outwardly away from the distal end to define an inlet that is larger than and communicates with the lumen, the expandable member sized to engage a wall of a body lumen within which the expandable member is expanded; and an elongate treatment member (82, 82') insertable through the lumen and comprising an expandable treatment element (86, 86') selectively expandable for directing obstructive material within a body lumen into the tubular member lumen through the inlet in the expandable member; wherein the expandable member comprises an outer annular membrane surrounding an inner annular membrane, the outer and inner membranes being formed as separate sleeves of material, the outer and inner membranes being attached together and to the tubular member distal end such that the outer and inner membranes together define an enclosed interior, the elongate tubular member comprising an inflation lumen communicating with the interior such that, when inflation media is delivered via the inflation lumen into the interior, the expandable member is expanded to the expanded configuration; wherein the proximal end of the outer membrane is attached to an outer surface of the distal end of the tubular member at a first location and wherein the proximal end of the inner membrane is butted to the distal end of the tubular member at a second location distal to the first location; and wherein the outer membrane has a greater axial length than the inner member such that proximal ends of the outer and inner membranes are spaced apart from one another along the distal end of the tubular member. an elongate tubular member comprising a proximal end, a distal end sized for introduction into a body lumen, a lumen extending between the proximal and distal ends, and an annular expandable member on the distal end that is expandable from a collapsed configuration to an expanded configuration wherein the expandable member adopts a tapered shape that flares outwardly away from the distal end to define an inlet that is larger than and communicates with the lumen, the expandable member sized to engage a wall of a body lumen within which the expandable member is expanded; and an elongate treatment member (82, 82') insertable through the lumen and comprising an expandable treatment element (86, 86') selectively expandable for directing obstructive material within a body lumen into the tubular member lumen through the inlet in the expandable member; wherein the expandable member comprises an outer annular membrane surrounding an inner annular membrane, the outer and inner membranes being formed as separate sleeves of material, the outer and inner membranes being attached together and to the tubular member distal end such that the outer and inner membranes together define an enclosed interior, the elongate tubular member comprising an inflation lumen communicating with the interior such that, when inflation media is delivered via the inflation lumen into the interior, the expandable member is expanded to the expanded configuration; wherein the proximal end of the outer membrane is attached to an outer surface of the distal end of the tubular member at a first location and wherein the proximal end of the inner membrane is butted to the distal end of the tubular member at a second location distal to the first location; and wherein the outer membrane has a greater axial length than the inner member such that proximal ends of the outer and inner membranes are spaced apart from one another along the distal end of the tubular member.