AMX Zintl compounds, crystallizing in several closely related layered structures, have recently garnered attention due to their exciting thermoelectric properties. In this study, we show that orthorhombic CaAgSb can be alloyed with hexagonal CaAgBi to achieve a solid solution with a structural transformation at x ∼ 0.8. This transition can be seen as a switch from three-dimensional (3D) to two-dimensional (2D) covalent bonding in which the interlayer M-X bond distances expand while the in-plane M-X distances contract. Measurements of the elastic moduli reveal that CaAgSb1-xBix becomes softer with increasing Bi content, with the exception of a steplike 10% stiffening observed at the 3D-to-2D phase transition. Thermoelectric transport measurements reveal promising Hall mobility and a peak zT of 0.47 at 620 K for intrinsic CaAgSb, which is higher than those in previous reports for unmodified CaAgSb. However, alloying with Bi was found to increase the hole concentration beyond the optimal value, effectively lowering the zT. Interestingly, analysis of the thermal conductivity and electrical conductivity suggests that the Bi-rich alloys are low Lorenz-number (L) materials, with estimated values of L well below the nondegenerate limit of L = 1.5 × 10-8 W Ω K-2, in spite of the metallic-like transport properties. A low Lorenz number decouples lattice and electronic thermal conductivities, providing greater flexibility for enhancing thermoelectric properties.