In this paper, we consider a class of constrained systems named double upper bounds $(p,q)$-constrained systems ($(p,q)$-DUB systems in brief), which are one-dimensional subshifts of finite type. We determinate the topological entropies (Shannon capacities) $C(p,q)$ of all $(p,q)$-DUB systems and consequently order all $(p,q)$-DUB systems according to the size of topological entropies. In particular, $C(p, \infty)=C(p+1, p+1)$ are the only equalities possible among the topological entropies of $(p,q)$-DUB systems.