A method is proposed which aims at reducing the numbers of look-up table (LUT) elements in logic circuits of Mealy finite state machines (FSMs). The FSMs with twofold state assignment are discussed. The reduction is achieved due to using two cores of LUTs for generating partial Boolean functions. One core is based on maximum binary state codes. The second core uses extended state codes. Such an approach allows reducing the number of LUTs in the block of state codes’ transformation. The proposed approach leads to LUT-based Mealy FSM circuits having three levels of logic blocks. Each partial function for any core is represented by a single-LUT circuit. A formal method is proposed for redistribution of states between these cores. An example of synthesis is shown to explain peculiarities of the proposed method. An example of state redistribution is given. The results of experiments conducted with standard benchmarks show that the double-core approach produces LUT-based FSM circuits with better area-temporal characteristics than they are for circuits produced by other investigated methods (Auto and One-hot of Vivado, JEDI, and twofold state assignment). Both the LUT counts and maximum operating frequencies are improved. The gain in LUT counts varies from 5.74% to 36.92%, and the gain in frequency varies from 5.42% to 12.4%. These improvements are connected with a very small growth of the power consumption (less than 1%). The advantages of the proposed approach increase as the number of FSM inputs and states increases.