A drilling rig having a top drive has a pipe gripper with a mandrel having an upper end for connection to and rotation with a drive string extending downward from the top drive. The pipe gripper has gripping elements that move radially into engagement with a string of pipe. A pull-down mechanism is mounted to the rig and secured to a non-rotating portion of the pipe gripper for exerting a downward force on the mandrel. A sensor is operatively coupled to the top drive to sense weight being supported by the top drive. A controller is linked to the sensor and the pull-down mechanism for controlling the downward force exerted on the mandrel by the pull-down mechanism in response to the weight sensed by the sensor.