Depends why you are slowing down.

On a motorway when you need to lose a few mph you use engine braking - unless you want people behind to *know* you are braking (eg if you've seen stopped/slow traffic)

I've you're going hell for leather on the twisty stuff then you brake and drop a gear or so - but that's as much about keeping the engine at the right revs for whatever you're doing as anything else.

I'd say you never drop a gear *just* to slow down in normal driving (aparently this came about when clutches were cheaper than brakes) - and I can think of times I do it.

Of course if you are about to slow down and you're at a change-up point then don't change up and let the engine slow you.

If you think you can drive with a hard and fast set of rules though you ought to ask why computers don't drive cars yet

Easy.

LBT
(of course I drive a TVR Tuscan - better known as "the one in Swordfish" - so what do I know )