Multi Engine and the precautionary shut down.

So imagine cruising at 9500 feet in a light twin when your passenger taps you on your shoulder and asks you what that black stuff is leaking out of the cowl.  You look at the oil pressure gauge and realize your day is about to get complicated.  What to do?  Do you wait for the engine to seize or shut it down while you still have a fighting chance?  Silly question isn't it.  But some pilots have never been tough what to do in this situation.  This scenario is a perfect situation to teach the precautionary shut down.  In most twins, if you follow the check list you will not have any problems  but there seems to be one important step that is continuously missed.  And that is to add power to the operating engine.  I've seen several people decide to shut down the offending engine but neglect to add power to the good one.  We end up loosing altitude unnecessarily  or, worse yet, trying to hold altitude while sacrificing airspeed.   Once we get behind the power curve on a twin, its hard to get back.  I've even seen pilots get dangerously close to Vmc. 

Remember how you where trained!  The instructor would fail an engine and you would respond: Mixtures, Props, throttles all forward, Flaps up, Gear up, Identify, Verify and Feather the dead engine.  Between each step  you where reminded to relax and fly the airplane.  That meant maintain heading, altitude and airspeed.  If you couldn't  hold altitude then you drifted down at Vyse.