A system for anchoring a distal end of a catheter at a treatment site includes an elongated catheter shaft that is formed with a lumen and two cone shaped balloon membranes. For the system, the proximal and distal ends of the balloon membranes are affixed to an outer surface of the shaft to establish balloons having inflation chambers between the membranes and the shaft. A first membrane portion of a first balloon membrane extends from the distal end of the membrane end to a balloon membrane midsection and a second membrane portion extends from the midsection to the proximal membrane end. To establish the proper shape for the inflated balloon, the second membrane portion is configured to establish a cone angle, α, (relative to a proximally directed portion of the longitudinal axis) that is less than or equal to ninety degrees (α≦90 degrees).
