  We report the angular diameter measurements of seven classical Cepheids (X
Sgr, eta Aql, W Sgr, zeta Gem, beta Dor, Y Oph and L Car) that we have obtained
with the VINCI instrument, installed at ESO's VLT Interferometer (VLTI). We
also present reprocessed archive data obtained with the FLUOR/IOTA instrument
on zeta Gem, in order to improve the phase coverage of our observations. We
obtain average limb darkened angular diameter values of LD(X Sgr) = 1.471 +/-
0.033 mas, LD(eta Aql) = 1.839 +/- 0.028 mas, LD(W Sgr) = 1.312 +/- 0.029 mas,
LD(beta Dor) = 1.891 +/- 0.024 mas, LD(zeta Gem) =1.747 +/- 0.061 mas, LD(Y
Oph) = 1.437 +/- 0.040 mas and LD(L Car) = 2.988 +/- 0.012 mas. For four of
these stars (eta Aql, W Sgr, beta Dor, and L Car) we detect the pulsational
variation of their angular diameter. This enables us to compute directly their
distances, using a modified version of the Baade-Wesselink method: d(eta Aql) =
276 [+55 -38] pc, d(W Sgr) = 379 [+216 -130] pc, d(beta Dor) = 345 [+175 -80]
pc, d(L Car) = 603 [+24 -19] pc. The stated error bars are statistical in
nature. Applying a hybrid method, that makes use of the Gieren et al. (1998)
Period-Radius relation to estimate the linear diameters, we obtain the
following distances (statistical and systematic error bars are mentioned): d(X
Sgr) = 324 +/- 7 +/- 17 pc, d(eta Aql) = 264 +/- 4 +/- 14 pc, d(W Sgr) = 386
+/- 9 +/- 21 pc, d(beta Dor) = 326 +/- 4 +/- 19 pc, d(zeta Gem) = 360 +/- 13
+/- 22 pc, d(Y Oph) = 648 +/- 17 +/- 47 pc and d(L Car) = 542 +/- 2 +/- 49 pc.
