  In spite of the relevance of Classical Cepheids as primary distance
indicators, a general consensus on the dependence of the Period-Luminosity (PL)
relation on the Cepheid chemical composition has not been achieved yet. From
the theoretical point of view, our previous investigations were able to
reproduce some empirical tests for suitable assumptions on the helium to metal
relative enrichment, but those results relied on specific assumptions
concerning the Mass-Luminosity relation and the efficiency of the convective
transfer in the pulsating envelopes. In this paper, we investigate the effects
of the assumed value of the mixing length parameter l/Hp on the pulsation
properties and we release the assumption of a fixed Mass-Luminosity relation.
As a whole, we show that our pulsation relations appear fully consistent with
the observed properties of Galactic and Magellanic Cloud Cepheids, supporting
the predicted steepening and brightening of the PL relations when moving from
metal-rich to metal-poor variables. Moreover, we show that the distances
inferred by the predicted PW relations agree with recently measured
trigonometric parallaxes, whereas they suggest a correction to the values based
on the Infrared Surface Brightness technique, as already found from an
independent method. Finally, also the pulsation metal contents suggested by the
predicted PW relations appear in statistical agreement with spectroscopic
[Fe/H] measurements.
