Purpose: Covariance between gray-matter measurements can reflect structural or functional brain networks though it has also been shown to be influenced by confounding factors (e.g., age, head size, and scanner), which could lead to lower mapping precision (increased size of associated clusters) and create distal false positives associations in mass-univariate vertexwise analyses. Approach: We evaluated this concern by performing state-of-the-art mass-univariate analyses (general linear model, GLM) on traits simulated from real vertex-wise gray matter data (including cortical and subcortical thickness and surface area). We contrasted the results with those from linear mixed models (LMMs), which have been shown to overcome similar issues in omics association studies. Results: We showed that when performed on a large sample (N ¼ 8662, UK Biobank), GLMs yielded greatly inflated false positive rate (cluster false discovery rate >0.6). We showed that LMMs resulted in more parsimonious results: smaller clusters and reduced false positive rate but at a cost of increased computation. Next, we performed mass-univariate association analyses on five real UKB traits (age, sex, BMI, fluid intelligence, and smoking status) and LMM yielded fewer and more localized associations. We identified 19 significant clusters displaying small associations with age, sex, and BMI, which suggest a complex architecture of at least dozens of associated areas with those phenotypes. Conclusions: The published literature could contain a large proportion of redundant (possibly confounded) associations that are largely prevented using LMMs. The parsimony of LMMs results from controlling for the joint effect of all vertices, which prevents local and distal redundant associations from reaching significance.