To continue dialogue over proposed Australian trials of Trap-Neuter-Return (TNR), we applied a framework requiring identification of areas of agreement, areas of disagreement, and identification of empirical data collection required to resolve disagreements. There is agreement that Australia has a problem with stray cats, causing problems of impacts on wildlife, nuisance, disease transmission (including public health issues and exchange of diseases between stray cat and pet cat populations), poor welfare outcomes for stray cats, and an emotional burden on staff euthanising healthy stray cats. There is disagreement on whether (i) current measures are failing, leading to unacceptably high euthanasia levels, (ii) some contributors to the debate misunderstand TNR, (iii) TNR trials will reduce urban cat populations and associated problems, (iv) TNR is an ethical solution to cat overpopulation, and (v) some contributors to the debate promulgated misinformation. Although not everyone agrees that TNR trials should proceed, as a hypothetical exploration, we propose an experimental approach explicitly comparing TNR to alternatives. Trials could only be considered if other detailed and well-funded attempts at stray cat control focusing across an entire Local Government Area (LGA) prove ineffective.