That's all there is!
there isn't any. more.
firstly, with transmission, Ppri=Psec. knowing that, VpriIpri=VsecIsec. increasing current means you get more e- 'sloshing' around the coil hence more resistance, hence greater power loss. Ploss is denoted by P=I^2 x R. Increasing current increases losses exponentially and you dont want that since it ^ costs.
secondly, knowing the above, If you decrease current, whilst MAINTAINING power value, (P=VI), then P can only be constant IF V is 'stepped up' or 'increased' since you've decreased current to avoid great loss of P. hope that makes sense.
p.s. i wouldnt be surprised if tsfx comes to this thread and asks for the removal of this. i doubt any1 here would report you, but yeah tsfx has long arms. i went to the lecture myself and greg wilmoth is the best lecturer there is. you shoulda gone. =p)