The period–luminosity (PL) relation is usually derived using time-averaged magnitudes, which require multiple-epoch observations to determine periods and adequately sample the light curves. Although single-epoch observations are more practical and require significantly less observational effort, they inherently introduce greater photometric scatter, leading to an increased dispersion in the derived PL relations. In this paper, we explore, in detail, a method that transforms single random-phase data to their mean-light values, using information obtained in other bands for the same Cepheid. This approach enables the accurate reconstruction of mean-light PL relations for wavelengths observed with space-based facilities, for instance, where the number of epochs per star makes simple averaging or template fitting less than optimal, with the latter requiring very high-precision periods for predictive phasing. While applying this technique across multiple bands, from optical to mid-IR, we focus particularly on widely separated bands covering the mid-IR to the optical. We showcase this method using the J band (as being observed by JWST) as the random-phase component. Our results show that this correction reduces the scatter of the PL relation in the J band by a factor of approximately 0.7×, equivalent to increasing the number of random-phase observations by a factor of 10, needed to obtain the same increase in precision as delivered here.