A system that controls the speed of a marine vessel includes first and second propulsion devices that produce first and second thrusts to propel the marine vessel. A control circuit controls orientation of the first and second propulsion devices about respective steering axes to control directions of the first and second thrusts. A first user input device is moveable between a neutral position and a non-neutral detent position. When a second user input device is actuated while the first user input device is in the detent position, the control circuit does one or more of the following so as to control the speed of the marine vessel: varies a speed of a first engine of the first propulsion device and a speed of a second engine of the second propulsion device; and varies one or more alternative operating conditions of the first and second propulsion devices.