Even though it has been proved that a fully thermally coupled distillation (TCD) system minimizes the energy used by a sequence of columns, it is well-known that vapor/liquid transfers between different sections produce an unavoidable excess of vapor (liquid) in some of them, increasing both the investment and operating costs. It is proposed here to take advantage of this situation by extracting the extra vapor/liquid and subjecting it to a direct/reverse vapor compression cycle. This new arrangement restores the optimal operating conditions of some of the affected sections with energy savings of around 20-30% compared with conventional TCD columns. Various examples, including the direct and reverse vapor recompression cycles, are presented. Furthermore, in each example, all possible modes of distillation (direct, indirect and Petlyuk distillation) with and without vapor recompression cycles (VRC) are compared to ensure that this approach delivers the best results. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 3767-3781, 2013