In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures with minimum arc-length $ge 4$. Let ${sf T}_{k,sigma}^{[4]} (n)$ denote the number of these structures. We derive exact enumeration results by computing the generating function ${bf T}_{k,sigma}^{[4]}(z)= sum_n{sf T}_{k,sigma}^{[4]}(n)z^n$ and derive the asymptotic formulas ${sf T}_{k,3}^{[4]}(n)^{}sim c_k n^{-(k-1)^2-frac{k-1}{2}} (gamma_{k,3}^{[4]})^{-n}$ for $k=3,...,9$. In particular we have for $k=3$, ${sf T}_{3,3}^{[4]}(n)^{}sim c_3 n^{-5} 2.0348^n$. Our results prove that the set of biophysically relevant RNA pseudoknot structures is surprisingly small and suggest a new structure class as target for prediction algorithms.
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