New radii, derived from a modified version of the Baade-Wesselink (BW) method that is tied to published KHG narrowband spectrophotometry, are presented for 13 bright Cepheids. The data yield a best-fitting period-radius relation given by log R/R = 1.071(±0.025) + 0.747(±0.028) log P₀. In combination with other high-quality radius estimates recently published by Laney & Stobie, the new data yield a period-radius relation described by log R/R = 1.064(±0.0006) + 0.750(±0.006) log P₀, which simplifies to R ∝ P^3/4. The relationship is used to test the scale of Cepheid luminosities inferred from cluster zero-age main-sequence (ZAMS) fitting, for which we present an updated list of calibrating Cepheids located in stellar groups. The cluster ZAMS-fitting distance scale tied to a Pleiades distance modulus of 5.56 is found to agree closely with the distance scale defined by Hipparcos parallaxes of cluster Cepheids and also yields Cepheid luminosities that are a good match to those inferred from the period-radius relation. The mean difference between absolute visual magnitudes based on cluster ZAMS fitting, M_VC, and those inferred for 23 cluster Cepheids from radius and effective temperature estimates, M_VBW, in the sense of C - BW is +0.019 ± 0.029 s.e. There is no evidence to indicate the need for a major revision to the Cepheid cluster distance scale. The absolute magnitude differences are examined using available [Fe/H] data for the cluster Cepheid sample to test the metallicity dependence of the period-luminosity relation. Large scatter and a small range of metallicities hinder a reliable estimate of the exact relationship, although the data are fairly consistent with predictions from stellar evolutionary models. The derived dependence is ΔM_V(C - BW) = +0.06(±0.03) - 0.43(±0.54)[ Fe/H].