  In this paper we study $k$-noncrossing RNA structures with minimum arc-length
4 and at most $k-1$ mutually crossing bonds. Let ${\sf T}_{k}^{[4]}(n)$ denote
the number of $k$-noncrossing RNA structures with arc-length $\ge 4$ over $n$
vertices. We prove (a) a functional equation for the generating function
$\sum_{n\ge 0}{\sf T}_{k}^{[4]}(n)z^n$ and (b) derive for $k\le 9$ the
asymptotic formula ${\sf T}_{k}^{[4]}(n)\sim c_k n^{-((k-1)^2+(k-1)/2)}
\gamma_k^{-n}$. Furthermore we explicitly compute the exponential growth rates
$\gamma_k^{-1}$ and asymptotic formulas for $4\le k\le 9$.
