A catheter that provides bi-directional steering and allows for deflection sensitivity adjustment includes a catheter body, a deflectable tip section and a control handle, wherein the control handle has a deflection member adapted for user manipulation, a deflection assembly responsive to the deflection member to draw on a tensile puller member for deflecting the tip section, and an adjustment mechanism adapted to adjust sensitivity of the deflection member. The adjustment mechanism also correspondingly adjusts a maximum degree of deflection of the tip section. The deflection assembly includes a rotatable pulley arm and two pulleys, and a deflection sensitivity adjustment mechanism with a cam device that varies a separation distance between the pulleys. The cam device is internally located in the pulley arm and is rotatable via deflection sensitivity knob by the user to increase the separation distance for greater deflection sensitivity in a deflection member user interface, or to decrease the separation distance for greater maximum degree of tip deflection.