We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation
\[
◻
u
=
−
u
5
\Box u = -u^5
\]
on
R
3
+
1
\mathbb {R}^{3+1}
constructed in Krieger, Schlag, and Tartaru (“Slow blow-up solutions for the
H
1
(
R
3
)
H^1(\mathbb {R}^3)
critical focusing semilinear wave equation”, 2009) and Krieger and Schlag (“Full range of blow up exponents for the quintic wave equation in three dimensions”, 2014) are stable along a co-dimension one Lipschitz manifold of data perturbations in a suitable topology, provided the scaling parameter
λ
(
t
)
=
t
−
1
−
ν
\lambda (t) = t^{-1-\nu }
is sufficiently close to the self-similar rate, i. e.,
ν
>
0
\nu >0
is sufficiently small. This result is qualitatively optimal in light of the result of Krieger, Nakamishi, and Schlag (“Center-stable manifold of the ground state in the energy space for the critical wave equation”, 2015). The paper builds on the analysis of Krieger and Wong (“On type I blow-up formation for the critical NLW”, 2014).