The present invention relates generally to a weapon having an eccentrically-pivoted barrel (1) that is mounted on a movable base (2), and to a method of elevating and stabilizing such a barrel. A drive mechanism (3) acts between the barrel and the base to permit and enable the elevation of the barrel relative to the base to be selectively changed. A compensation device acts between the barrel and base to compensate for the unbalance of the barrel. The compensation device includes a gyroscope (13) mounted on the barrel and arranged to provide an output signal, a set point generator (12), a closed-loop control device (10) and an actuating element (16). The actual position of the barrel is sensed by the gyroscope, which supplies its output signal to the set point generator. The set point generator produces a set force value as a function of the gyroscope output signal. The set force value is supplied to the closed-loop control device, which produces a set point value that is, in turn, supplied to the actuator for controllably changing the elevation of the barrel.