Frequent use of the engine telegraph is not unusual when manoeuvring in and out of harbours, or navigating through a narrow waterway. The captain may let the ship proceed by herself with the propeller idling, brake her by reversing the propeller, or actuate the engine shortly with the helm hard-over to correct the heading. Naturally, these operations cause a significant headway change, and at the same time introduce quite an extensive variation in propeller slip, which considerably affects the rudder effectiveness. We reduced the well-known coupled equations of forward, sway and yaw motion of a ship, Eq. (2. 1), into a simple mathematical model of ship response in such manoeuvres. Those are Eqs. (2. 10), (2. 20) and (2. 25). We make use of the existing knowledge on the rudder-to-yaw response in steady steaming as well as of a somewhat modified self-propulsion tank test to determine the propeller performance. The effect of propeller slip on the rudder effectiveness and the hydrodynamic force exerted by a reversing propeller are also investigated. According to the free-sailing model experiments, two VLCCs and one container ship model, the present simple mathematical model of ship response proved successful.