We present a study of the trends in luminosity, linear size, spectral index, and redshift of classical double radio sources, from three complete samples selected at successively fainter low radio-frequency flux limits. We have been able to decouple the effects of the tight correlation between redshift and luminosity (inherent in any single flux-limited sample) which have hitherto hindered interpretation of the relationships between these four source properties. The major trends found are that (i) spectral indices increase with linear size, (ii) rest-frame spectral indices have a stronger dependence on luminosity than on redshift except at high (GHz) frequencies, and (iii) the linear sizes are smaller at higher redshifts. We reproduce the observed dependences in a model for radio sources (born throughout cosmic time according to a radio-source birth function) whose lobes are fed with a synchrotron-emitting population from compact hotspots, and which suffer inverse Compton, synchrotron, and adiabatic expansion losses. The magnetic energy density within each hotspot is proportional to the jet power, and synchrotron losses suffered in the hotspot mean that the energy spectrum of the emitting particles fed to the lobes is governed by the jet power. The axial ratios of radio sources in our model increase as the sources age, and axial ratios are higher in sources with higher jet power. In simulating the basic observed dependences, we find that there is no need to invoke any systematic change in the environments of these objects with redshift if the consequences of imposing a survey flux limit on our simulated data sets are properly included in the model. It is also necessary to include appropriate energy loss mechanisms (such as the effects of the cosmic microwave background and feeding the lobes from a compact hotspot), which cause decreasing luminosity through the life of a source. Although our study has broken the luminosity-redshift degeneracy, we present evidence that for such studies there is an unavoidable ``youth-redshift degeneracy,'' even though radio sources are short-lived relative to the age of the universe; it is imperative to take this into account in studies that seemingly reveal correlations of source properties with redshift such as the ``alignment effect.''