  Conditioning a branching Brownian motion to have an atypically low maximum
leads to a suppression of the branching mechanism. In this note, we consider a
branching Brownian motion conditioned to have a maximum below $\sqrt{2}\alpha
t$ ($\alpha<1$). We study the precise effects of an early/late first branching
time and a low/high first branching location under this condition. We do so by
imposing additional constraints on the first branching time and location. We
obtain large deviation estimates, as well as the optimal first branching time
and location given the additional constraints.
