  For 2 + 1 dimensional wave maps with $\mathbb{S}^2$ as the target, we show
that for all positive numbers $T_0 > 0$ and $E_0 > 0$, there exist Cauchy
initial data with energy at least $E_0$, so that the solution's life-span is at
least $[0,T_0]$. We assume neither symmetry nor closeness to harmonic maps.
