A bi-directional catheter with nearly double the throw in its catheter tip deflection defines a puller wire travel path having a U-turn a pulley which minimizes the offset angle between the puller wire and the longitudinal axis of the control handle while maximizing the travel distance of that puller wire for any given distance traveled by the pulley drawing the puller wire. In particular, the control handle of the catheter which includes a steering assembly having a lever arm carrying a pair of pulleys for drawing corresponding puller wires to deflect the tip section of the catheter. The pulleys are rotatably mounted on opposing portions of the lever arm such that one pulley is moved distally as the other pulley is moved proximally when the lever arm is rotated. Because each puller wire is trained on a respective pulley, rotation of the lever arm causes the pulley that is moved proximally to draw its puller wire to deflect the tip section in the direction of the off-axis lumen in which that puller wire extends.