Heat recuperation is often used to improve the overall cycle efficiency of standard gas turbines. Hereby a high heat exchanger effectiveness and low pressure drops are favourable to achieve maximal cycle efficiency. Finding a compromise between these conflicting requirements is the main challenge in recuperator design. In this paper it is shown that the optimal cold and hot side pressure drops of a micro recuperator are uniquely correlated when integrated in a gas turbine. For an optimized microchannel recuperator, the ratio of the cold side pressure drop over the hot side one is only a function of gas turbine properties and primarily depends on the compressor pressure ratio. Based on these findings, a simplified optimization procedure is applied to design a micro recuperator in a 1.5 kW gas turbine. It is shown that the results of this optimization are almost identical to the full multi-dimensional optimization with an accuracy of approximately 1% on geometrical parameters and an excellent agreement for cycle efficiency.