  (ABRIDGED) We have applied the near-IR Barnes-Evans realization of the
Baade-Wesselink method as calibrated by Fouque & Gieren (1997) to five
metal-poor Cepheids with periods between 13 and 17 days in the Small Magellanic
Cloud as well as to a sample of 34 Galactic Cepheids to determine the effect of
metallicity on the period-luminosity (P-L) relation. For ten of the Galactic
Cepheids we present new accurate and well sampled radial-velocity curves. The
Baade-Wesselink analysis provides accurate individual distances and
luminosities to the Cepheids in the two samples, allowing us to constrain
directly, in a purely differential way, the metallicity effect on the Cepheid
P-L relation. For the Galactic Cepheids we provide a new set of P-L relations
which have zero-points in excellent agreement with astrometric and
interferometric determinations. These relations can be used directly for the
determination of distances to solar-metallicity samples of Cepheids in distant
galaxies, circumventing any corrections for metallicity effects on the
zero-point and slope of the P-L relation. We find evidence for both such
metallicity effects in our data. Comparing our two samples of Cepheids at a
mean period of about 15 days, we find a weak effect of metallicity on the
luminosity similar to that adopted by the HST Key Project on the Extragalactic
Distance Scale.
