  We show that the modulus of continuity of the SLE$_4$ uniformizing map is
given by $(\log \delta^{-1})^{-1/3+o(1)}$ as $\delta \to 0$. As a consequence
of our analysis, we show that the Jones-Smirnov condition for conformal
removability (with quasihyperbolic geodesics) does not hold for SLE$_4$. We
also show that the modulus of continuity for SLE$_8$ with the capacity time
parameterization is given by $(\log \delta^{-1})^{-1/4+o(1)}$ as $\delta \to
0$, proving a conjecture of Alvisio and Lawler.
