Controlling the charge and spin degrees of freedom of electrons in solids has been at the heart of condensed-matter science for centuries. One hallmark of metallic conduction is the Wiedemann-Franz law which implies that a moving charge carries entropy. Despite centuries of dedicated research, disentangling charge and heat transport has remained an unsolved issue so far. Here we present a direct route to reduce thermal conductivity of conduction electrons with respect to their electrical conductivity via energy-dependent scattering. By constraining electronic transport to a boxcar-type distribution asymmetrically around the Fermi energy, a large Seebeck coefficient and electrical conductivity can be realized simultaneously while electronic heat conduction is suppressed. Based on the case of monolayer Ni₃In, which comprises two flat bands around the Fermi energy, we propose flat-band systems as a promising, tunable platform for scattering phase space engineering. Besides this novel approach, our large-scale assessment of ≈ 5× 10⁴ data sets in a 'Wiedemann-Franz plot' of zT vs. S² provides an effective tool to identify reports of L≪ L₀ from literature - pointing towards either new and interesting physical mechanisms - or overlooked measurement artifacts.