We present a phenomenological procedure of dealing with the COVID--19 data provided by government health agencies of eleven different countries. Instead of using the (exact or approximate) solutions to the SIR (or other) model(s) to fit the data by adjusting the time--independent parameters included in those models, we introduce dynamical parameters whose time--dependence may be phenomenologically obtained by adequately extrapolating a chosen subset of the daily provided data. This phenomenological approach works extremely well to properly adjust the number of infected (and removed) individuals in time, for the countries we consider. Besides, it can handle the sub--epidemic events that some countries may experience. In this way, we obtain the evolution of the pandemic without using any a priori model based on differential equations.