  We study a branching Brownian motion $Z$ with a generic branching law,
evolving in $\mathbb{R}^d$, where a field of Poissonian traps is present. Each
trap is a ball with constant radius. We focus on two cases of Poissonian
fields: a uniform field and a radially decaying field. Using classical results
on the convergence of the speed of branching Brownian motion, we establish
precise results on the population size of $Z$, given that it avoids the trap
field, while staying alive up to time $t$. The results are stated so that each
gives an 'optimal survival strategy' for $Z$. As corollaries of the results
concerning the population size, we prove several other optimal survival
strategies concerning the range of $Z$, and the size and position of clearings
in $\mathbb{R}^d$. We also prove a result about the hitting time of a single
trap by a branching system (Lemma 1), which may be useful in a completely
generic setting too. Inter alia, we answer some open problems raised in [Mark.
Proc. Rel. Fields, 9 (2003), 363 - 389].
