An intravascular catheter carries a helical reinforcement member embedded within at least a portion of the tubular wall of the catheter. The helical reinforcement member comprises a helical first portion having coils of greater pitch than the pitch of helical coils of a second portion. Preferably, the catheter is for insertion into brain arteries, and comprises a flexible tube having an outer diameter of no more that about 0.05 inch, for example 3 French or smaller. The flexible tube defines outer and inner tubular layers. The inner tubular layer surrounds a catheter lumen and comprises chemically inert fluorinated polymer such as PTFE. The outer tubular layer comprises at least three longitudinally spaced, connected tubular sections. The sections are of successively increasing flexibility from the proximal toward the distal catheter end. Also, manufacturing methods are disclosed pertaining to increasing the flexibility of a section of the catheter and joining together in abutting relation a pair of dissimilar catheter reinforcement members.