A systematic rational search for newly designed melatonin derivatives, was performed using a computer-assisted protocol. A total of 116 derivatives were generated by adding functional groups (i.e., -OH, -NH2, -SH and -COOH) to the melatonin structure. A selection score (SS) was built to sample the search space, simultaneously considering ADME (absorption, distribution, metabolism, excretion) properties, toxicity and manufacturability (i.e., synthetic accessibility). The search characterized the whole set of designed melatonin derivatives and allowed the selection of a reduced subset of 20 melatonin derivatives that are expected to be the most promising, regarding drug-like behavior. For this subset, several reactivity indices were estimated, as well as their pKa values. According to the gathered data, 5 melatonin derivatives have been identified as the most likely candidates to act as chemical antioxidant (directly scavenging free radicals, by electron transfer and/or H transfer). All of them are predicted to be better for that purpose than melatonin itself or trolox (water soluble vitamin E analog). The findings from this work are expected to motivate further investigations on these molecules, using both theoretical and experimental approaches.