An outboard motor and a method of making an outboard motor provide an exhaust conduit having a first end that receives exhaust gas from an internal combustion engine and a second end that discharges exhaust gas to seawater via a propeller shaft housing outlet. An exhaust conduit opening is formed in the exhaust conduit between the first and second ends. The exhaust conduit opening is for discharging exhaust gas from the exhaust conduit to atmosphere via a driveshaft housing of the outboard motor and via an idle exhaust relief outlet and a driveshaft housing outlet in the driveshaft housing. The driveshaft housing outlet is vertically located between the propeller shaft housing outlet and the idle exhaust relief outlet. A cooling pump pumps cooling water from a cooling water inlet for cooling the internal combustion engine to a cooling water outlet for discharging cooling water from the outboard motor. The exhaust conduit opening and cooling water outlet are configured such that the cooling water collects by gravity in the driveshaft housing to a level that is above the exhaust conduit opening.