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In this paper we present our computational experience with a heuristic for the problem of minimizing fuel cost on steady-state gas transmission problems on cyclic networks. The procedure is based on a two-stage iterative procedure, where, in a given iteration, gas flow variables are fixed and optimal pressure variables are found via dynamic programming in the first stage. In the second stage, the pressure variables are fixed and an attempt is made to find a set of flow variables that improve the objective function by exploiting the underlying network structure. This work focuses on cyclic network topologies, that is, networks with at least one cycle containing two or more compressor stations. This kind of topologies posses the highest degree of difficulty in real-world problems.