The present invention provides a bi-directional catheter with nearly double the throw in its catheter tip deflection. In particular, the travel path of each the puller wire includes a U-turn or doubling-back around 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 one embodiment, the catheter has an elongated catheter body, a catheter tip section with first and second diametrically-opposed off-axis lumens, and a control handle which includes a steering assembly having a lever structure carrying a pair of pulleys for simultaneously drawing and releasing corresponding puller wires to deflect the tip section of the catheter.