  We have used the infrared surface brightness technique to obtain a new
absolute calibration of the Cepheid PL relation in optical and near-infrared
bands from improved data on Galactic stars. The infrared surface brightness
distances to the Galactic variables are consistent with direct interferometric
Cepheid distance measurements, and with the PL calibration coming from
Hipparcos parallaxes of nearby Cepheids, but are more accurate than these
determinations. We find that in all bands, the Galactic Cepheid PL relation
appears to be slightly, but significantly steeper than the corresponding
relation defined by the LMC Cepheids. Since the slope of our LMC Cepheid sample
is clearly better defined than the one of the much smaller Galactic sample, we
fit the LMC slopes to our Galactic calibrating Cepheid sample (which introduces
only a small uncertainty) to obtain our final, adopted and improved absolute
calibrations of the Cepheid PL relations in the VIWJHK bands. Comparing the
absolute magnitudes of 10-day period Cepheids in both galaxies which are only
slightly affected by the different Galactic and LMC slopes of the PL relation,
we derive values for the LMC distance modulus in all these bands which can be
made to agree extremely well under reasonable assumptions for both, the
reddening law, and the adopted reddenings of the LMC Cepheids. This yields, as
our current best estimate from Cepheid variables, a LMC distance modulus of
18.55 +- 0.06.
