Abstract The correlation of the diagnostic indices FTI and T 4/TBG with actual free T 4 levels (FT 4) was investigated by numerical analysis. It was shown that, FT 4 being kept constant, both indices vary with altered TBG concentrations. Thus neither index is truly proportional to FT 4. In this respect both indices appear doubtful tools for diagnosing patients with abnormal TBG levels. A “map” constructed by plotting T 4 versus T 3U appeared to offer a higher discriminatory potential with respect to pathologic FT 4 values. Such an idealized map was shown to consist of hypo-, eu- and hyperthyroid domains separated by lines governed by the limit values of the FT 4 normal range. In practice, of course, these domains are separated by border regions rather than border lines and they should be derived from clinical data.