Aiming to increase sustainability in the field of construction, this study investigates possible alternative materials, considered as by-products, for the manufacture of greener low-strength concretes, intended for the manufacture of Concrete Masonry Units (CMUs); using sawdust in replacement of sand and wood ash and lime mud in replacement of cement. The by-products are characterized by means of physical and chemical analyses, to determine their potential use in concrete; then ten different concrete mixes, each with different amounts of by-products, and a reference concrete are tested. The effects of these by-products on the density, absorption, voids, compressive strength, thermal conductivity, thermal diffusivity, and specific heat of the concrete are all investigated.