A system of devices for performing a medical procedure at a treatment site in a cerebral vessel of a patient, the system comprising: a catheter having a catheter lumen having an inner diameter and a distal end; and an inner member sized to slide within the catheter lumen, the inner member comprising: a single lumen having a distal opening; a flexible distal region of variable stiffness which increases from a distal section thereof constructed of a softer material to a proximal section thereof constructed with a stiffer material, and wherein the flexible distal region comprises a first outer diameter that tapers distally to a second outer diameter that is smaller than the first outer diameter, the first and second outer diameters being sized to minimize a mismatch between the inner diameter of the catheter and the outer diameter of a guidewire used with the system; and a flexible tubular extension coupled to and extending distally past the flexible distal region, wherein a length of the tubular extension has a uniform outer diameter and wherein the distal opening from the single lumen is at a distal-most end of the tubular extension, wherein the inner member is adapted to advance the catheter to the treatment site in the cerebral vessel. a catheter having a catheter lumen having an inner diameter and a distal end; and an inner member sized to slide within the catheter lumen, the inner member comprising: a single lumen having a distal opening; a flexible distal region of variable stiffness which increases from a distal section thereof constructed of a softer material to a proximal section thereof constructed with a stiffer material, and wherein the flexible distal region comprises a first outer diameter that tapers distally to a second outer diameter that is smaller than the first outer diameter, the first and second outer diameters being sized to minimize a mismatch between the inner a single lumen having a distal opening; a flexible distal region of variable stiffness which increases from a distal section thereof constructed of a softer material to a proximal section thereof constructed with a stiffer material, and wherein the flexible distal region comprises a first outer diameter that tapers distally to a second outer diameter that is smaller than the first outer diameter, the first and second outer diameters being sized to minimize a mismatch between the inner diameter of the catheter and the outer diameter of a guidewire used with the system; and a flexible tubular extension coupled to and extending distally past the flexible distal region, wherein a length of the tubular extension has a uniform outer diameter and wherein the distal opening from the single lumen is at a distal-most end of the tubular extension, wherein the inner member is adapted to advance the catheter to the treatment site in the cerebral vessel. a flexible tubular extension coupled to and extending distally past the flexible distal region, wherein a length of the tubular extension has a uniform outer diameter and wherein the distal opening from the single lumen is at a distal-most end of the tubular extension, wherein the inner member is adapted to advance the catheter to the treatment site in the cerebral vessel. <EOS>