Leaf venation is diverse across plant species and has practical applications from paleobotany to modern agriculture. However, the impact of vein traits on plant performance has not yet been tested in a model system such as Arabidopsis thaliana. Previous studies analysed cotyledons of A. thaliana vein mutants and identified visible differences in their vein systems from the wild type (WT). We measured leaf hydraulic conductance (Kleaf), vein traits, and xylem and mesophyll anatomy for A. thaliana WT (Col-0) and four vein mutants (dot3-111 and dot3-134, and cvp1-3 and cvp2-1). Mutant true leaves did not possess the qualitative venation anomalies previously shown in the cotyledons, but varied quantitatively in vein traits and leaf anatomy across genotypes. The WT had significantly higher mean Kleaf. Across all genotypes, there was a strong correlation of Kleaf with traits related to hydraulic conductance across the bundle sheath, as influenced by the number and radial diameter of bundle sheath cells and vein length per area. These findings support the hypothesis that vein traits influence Kleaf, indicating the usefulness of this mutant system for testing theory that was primarily established comparatively across species, and supports a strong role for the bundle sheath in influencing Kleaf.