A catheter is provided which is disposed for insertion into a fluid-containing cavity of a patient, such as a ventricle of the patient's brain, to drain CSF therefrom. The catheter includes an elongated body provided with a cross-section having an outer surface which is smooth and free of projections, angles or the like which could damage adjacent brain tissue. The elongated body is further provided with proximal and distal ends, a first lumen disposed to serve as a fluid flow passage, and a second lumen extending past a given position located on the elongated body. A titanium wire element is inserted into the second lumen for enabling a neurosurgeon to readily select and adjust the angular orientation between first and second catheter segments, wherein the first and second segments comprise the portions of the elongated body extending between the given position and the proximal and distal ends, respectively. Reinforcing structure is provided around the elongated body to prevent an end of the wire from pushing or rupturing therethrough.