Described herein are non-natural NAD+-dependent alcohol dehydrogenases (ADHs) capable of at least two fold greater conversion of methanol or ethanol to formaldehyde or acetaldehyde, respectively, as compared to its unmodified counterpart. Nucleic acids encoding the non-natural alcohol dehydrogenases, as well as expression constructs including the nucleic acids, and engineered cells comprising the nucleic acids or expression constructs are described. Also described are engineered cells expressing a non-natural NAD+-dependent alcohol dehydrogenase, optionally include one or more additional metabolic pathway transgene(s), methanol metabolic pathway genes, target product pathway genes, cell culture compositions including the cells, methods for promoting production of the target product or intermediate thereof from the cells, compositions including the target product or intermediate, and products made from the target product or intermediate.