  Suppose that $\eta$ is a whole-plane space-filling SLE$_\kappa$ for $\kappa
\in (4,8)$ from $\infty$ to $\infty$ parameterized by Lebesgue measure and
normalized so that $\eta(0) = 0$. For each $T > 0$ and $\kappa \in (4,8)$ we
let $\mu_{\kappa,T}$ denote the law of $\eta|_{[0,T]}$. We show for each $\nu,
T > 0$ that the family of laws $\mu_{\kappa,T}$ for $\kappa \in [4+\nu,8)$ is
compact in the weak topology associated with the space of probability measures
on continuous curves $[0,T] \to {\mathbf C}$ equipped with the uniform
distance. As a direct byproduct of this tightness result (taking a limit as
$\kappa \uparrow 8$), we obtain a new proof of the existence of the SLE$_8$
curve which does not build on the discrete uniform spanning tree scaling limit
of Lawler-Schramm-Werner.
