A steerable catheter includes control handle having a generally tubular housing with a longitudinal slot therein in which an axially or longitudinally movable tow-part slideblock resides, and a generally cylindrical, rotatably mounted thumbwheel surrounding a distal portion of the tubular housing, for controlling the axial translation of the slideblock. The pullwire passes into the distal end of the control handle and is only secured to the proximal part of the two-part slideblock so as to prevent the user from placing the pullwire under compression. A tip radius adjusting wire is attached to and extends distally from a slide actuator in the control handle into and through the main catheter shaft portion. The free distal end of the tip radius adjusting wire is selectably locatable at different positions. The radius of curvature of the tip portion, when deflected, depends upon how far distally into the deflectable tip portion the radius adjusting wire has been advanced by the user. The electrode catheter thus has a deflectable tip whose radius of curvature is adjustable over a relatively wide range.