Proponents of a basic income (BI) claim that, on top of many other benefits, it could bring significant reductions in financial poverty. Using microsimulation analysis in a comparative two-country setting, we show that the potential poverty-reducing impact of BI strongly depends on exactly how and where it is implemented. Implementing a BI requires far more choices than advocates seem to realise. The level at which a BI is set matters, but its exact specification matters even more. The impact of a BI, be it a low or a high one, also strongly depends on the characteristics of the system that it is (partially) replacing or complementing, as well as the socio-economic context in which it is introduced. Some versions of BI could potentially help to reduce poverty but always at a significant cost and with substantial sections of the population incurring significant losses, which matters for political feasibility. A partial BI complementing existing provisions appears to make more potential sense than a full BI replacing them. The simplicity of BI, however, tends to be vastly overstated.