  We prove that for almost every Brownian motion sample, the corresponding
SLE(\kappa) curves parameterized by capacity exist and change continuously in
the supremum norm when \kappa varies in the interval [0,\kappa_0), where
\kappa_0=8(2-\sqrt{3})=2.143... We estimate the \kappa-dependent modulus of
continuity of the curves and also give an estimate on the modulus of continuity
for the supremum norm change with \kappa.
