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Tuning space mapping (TSM) with embedded tuning elements allows efficient design of microwave circuits by substituting sections in the electromagnetic (EM) model with corresponding sections of designable equivalent elements. Parameters of these elements are subsequently tuned and their optimal values are “translated” into relevant changes of the original structure's design variables. Although this optimization process typically requires only a few iterations to complete, the simulation of the structure with a number of co-calibrated ports (required to insert the tuning elements) is substantially longer than that of the original structure. In this paper, we propose a fast TSM algorithm that exploits a reduced structure with significantly fewer co-calibrated ports for creating the tuning model. This results in dramatic reduction of the computational cost of the optimization process. Verification examples and comparison with the standard TSM are provided.