We consider the possibilities for prediction of liquid densities under pressure based on the inverse reduced fluctuations parameter, which is directly connected with the isothermal compressibility. This quantity can be determined based on the thermodynamic properties of the saturated liquid, and it consists of only two constant parameters within a relatively wide region close to the melting points. It is confirmed by the comparison with the experimental data on n -alkanes that the derived expression is a quite reasonable estimator without a necessity to fit data along some parts of isotherms for different temperatures. At the same time, the obtained formula (i) can be reduced to the form of the Tait equation and (ii) the resulting Tait parameters in this representation have a clear physical meaning as functions of the excess entropy, which determines the mentioned reduced fluctuations.