I disagree that it would be pointless. That's why it is important to know whether or not the 2nd offer removes the trigger.
I had a first rounder who rejected my first offer, but I really wanted the guy. His demads where higher than what I had left. I just offered what I had left and he kept rejecting....over and over again. Until finally, after the playoffs had started, he signed for my offer. I must have offered my max 30 or more times. If he would have rejected all the way until the end, I could tell you the answer to your question.
Ultimately I can't, but the bottom line is that lowballing a second demand is not necessarily pointless. I think knowing the answer to your question is vital in your situation, but I'm inclined to agree with Crump - that the rejection of initial demand is the trigger.