  The advantages of a near-infrared variant of the Barnes-Evans method for
estimating distances to Cepheid variables are described and quantified. A
surface brightness-color relation for $K$ photometry and the $(V-K)_0$ color
index is established using modern, high-precision angular diameters from
optical interferometers. Applied to data for the galactic (cluster) Cepheid U
Sgr, this method yields a distance of 0.660 $\pm$ 0.024 kpc and a true distance
modulus of 9.10 $\pm$ 0.07 mag. This estimate compares with the true distance
modulus of 9.37 $\pm$ 0.22 mag estimated by Gieren, Barnes, and Moffett (1993)
using the classical Barnes-Evans technique. The possibility of estimating
distances of LMC and SMC Cepheids directly -- without intermediate steps -- is
discussed. The feasibility of determining the distance of M31 or M33 using this
technique is examined and is probably within the reach of 8m-class telescopes.
