I'm confused on exactly what are you trying to say? What do you mean "deal with level flight?"
Yes, when you change power, you'll gain/lose airspeed, assuming you correct with pitch and trim corrections for the speed change, you can maintain altitude. Now say you pull the power, but don't change pitch, well you descend, vice versa with a power addition. In the end, there's not really a specific order, because most of these are done simutaniously as far as pitch/trim are concerned.
I'm just throwing out scenarios' to make sure we're on the same page, or maybe I'll cover it with all the randomness.