We present a new photometric method by which improved high-precision reddenings and true distance moduli can be determined to individual Galactic Cepheids once distance measurements are available. We illustrate that the relative positioning of stars in the Cepheid period-luminosity (PL) relation (Leavitt law) is preserved as a function of wavelength. This information then provides a powerful constraint for determining reddenings to individual Cepheids, as well as their distances. As a first step, we apply this method to the 59 Cepheids in the compilation of Fouque et al. Updated reddenings, distance moduli (or parallaxes), and absolute magnitudes in seven (optical through near-infrared) bands are given. From these intrinsic quantities, multiwavelength PL and color-color relations are derived. We find that the V-band period-luminosity-color relation has an rms scatter of only 0.06mag, so that individual Cepheid distances can be measured to 3%, compared with dispersions of 6 to 13% for the one-parameter K through B PL relations, respectively. This method will be especially useful in conjunction with the new accurate parallax sample upcoming from Gaia.