Bacteria possess networks of small RNAs (sRNAs) that are important for modulating gene expression. At the center of many of these sRNA networks is the Hfq protein. Hfqs role is to quickly match cognate sRNAs and target mRNAs from among a large number of possible combinations and anneal them to form duplexes. Here we show using a kinetic model that Hfq can efficiently and robustly achieve this difficult task by minimizing the sequestration of sRNAs and target mRNAs in Hfq complexes. This sequestration can be reduced by two non-mutually exclusive kinetic mechanisms. The first mechanism involves heterotropic cooperativity (where sRNA and target mRNA binding to Hfq is influenced by other RNAs bound to Hfq), this cooperativity can selectively decrease singly-bound Hfq complexes and ternary complexes with non-cognate sRNA-target mRNA pairs while increasing cognate ternary complexes. The second mechanism relies on frequent RNA dissociation enabling the rapid cycling of sRNAs and target mRNAs among different Hfq complexes, this increases the probability the cognate ternary complex forms before the sRNAs and target mRNAs degrade. We further demonstrate that the performance of sRNAs in isolation is not predictive of their performance within a network. These findings highlight the importance of experimentally characterizing duplex formation in physiologically relevant contexts with multiple RNAs competing for Hfq. The model will provide a valuable framework for guiding and interpreting these experiments.