D. Wechsler (2008b) reported confirmatory factor analyses (CFAs) with standardization data (ages 16-69 years) for 10 core and 5 supplemental subtests from the Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV). Analyses of the 15 subtests supported 4 hypothesized oblique factors (Verbal Comprehension, Working Memory, Perceptual Reasoning, and Processing Speed) but also revealed unexplained covariance between Block Design and Visual Puzzles (Perceptual Reasoning subtests). That covariance was not included in the final models. Instead, a path was added from Working Memory to Figure Weights (Perceptual Reasoning subtest) to improve fit and achieve a desired factor pattern. The present research with the same data (N = 1,800) showed that the path from Working Memory to Figure Weights increases the association between Working Memory and Matrix Reasoning. Specifying both paths improves model fit and largely eliminates unexplained covariance between Block Design and Visual Puzzles but with the undesirable consequence that Figure Weights and Matrix Reasoning are equally determined by Perceptual Reasoning and Working Memory. An alternative 4-factor model was proposed that explained theory-implied covariance between Block Design and Visual Puzzles and between Arithmetic and Figure Weights while maintaining compatibility with WAIS-IV Index structure. The proposed model compared favorably with a 5-factor model based on Cattell-Horn-Carroll theory. The present findings emphasize that covariance model comparisons should involve considerations of conceptual coherence and theoretical adherence in addition to statistical fit. (Contains 4 figures and 2 tables.)