  We prove that every immersed $C^2$-curve $\gamma$ in $\mathbb R^n$,
$n\geqslant 3$ with curvature $k_{\gamma}$ can be $C^1$-approximated by
immersed $C^2$-curves having prescribed curvature $k>k_{\gamma}$. The
approximating curves satisfy a $C^1$-dense $h$-principle. As an application we
obtain the existence of $C^2$-knots of arbitrary positive curvature in each
isotopy class, which generalizes a similar result by McAtee for $C^2$-knots of
constant curvature.
