It all comes down to nage not choosing the technique, but uke.. If complex is what's demanded by uke's attack, posture, size and maai then complex is what you do...
My 2p worth
David, check out thread called "Who decides?" in the "Aikido:General" forum here. This was the subject of a question I started the thread with.
P.S. 2p is actually worth more than 2 cents, thus a more valuable opinion!