When designing sparse flexibility structures, the long chain is the best candidate. Theoretical results and empirical evidence show that the long chain structure can achieve a really good performance. This performance is compromised when assumptions presented in the literature are relaxed. The most restrictive assumption when designing flexibility structures in real-world applications is that the demands in the network are identically distributed. In this paper we intend to relax that assumption and consider arbitrary demand distributions. We leverage our methodology on existing results and build sparse flexibility structure with at most O(2n) and O(3n). The proposed structures show promising results by achieving almost optimal performance over several systems with arbitrary distributions.