A mimicking network for a k-terminal network, N, is one whose realizable external flows are the same as those of N. Let S(k) denote the minimum size of a mimicking network for a k-terminal network. In this paper we give new constructions of mimicking networks and prove the following results (the values in brackets are the previously best known results): S(4)=5 [2¹⁶], S(5)=6 [2³²]. For bounded treewidth networks we show S(k)= O(k) [2^2<<72>>k], and for outerplanar networks we show S(k) £ 10k-6 [k²2^k+2]]]>.