  We compute the wig for the BTZ black hole, namely the complete non-linear
solution of supergravity equations with all fermionic zero modes. We use a
"gauge completion" method starting from AdS_3 Killing spinors to generate the
gravitinos fields associated to the BH and we compute the back-reaction on the
metric. Due to the anticommutative properties of the fermionic hairs the
resummation of these effects truncates at some order. We illustrate the
technique proposed in a precedent paper in a very explicit and analytical form.
We also compute the mass, the angular momentum and other charges with their
corrections.
