Veins are the main irrigation system of the leaf lamina and an understanding of the hydraulic architecture of the vein networks is essential for understanding leaf function. However, determination of leaf hydraulic parameters is challenging, because for most leaves the vein system is reticulate, contains a hierarchy of different vein sizes, and consists of leaky conduits. We present a new approach that allows for measurements of pressure differences between the petiole and any vein within the leaf. Measurements of Laurus nobilis leaves indicate that first- and second-order veins have high axial conductance and relatively small radial permeability, thus allowing water to reach distal areas of the leaf with only a small loss of water potential. Higher order veins tend to be more hydraulically resistant and permit greater radial leakage. This design allows for a relatively equitable distribution of water potential and thus reflects the capacity of the venation to provide a relatively homogeneous water supply across the leaf lamina, with only the leaf margins being hydraulically disadvantaged relative to the rest of the leaf.