The fact that nuclear waste is a problem waiting to be solved is perceived to be a matter of common sense worldwide. Nonetheless, the negative aspects of nuclear waste disposal often dominate public debate. This is also true in the German case of a currently planned deep geological repository (DGR) for high-level nuclear waste (HLW). In studies about risk and benefit perception one may wonder whether the positive aspects proposed by the literature are really part of people's mental models. To date, any positive aspects that the German public associates with a DGR are unknown. In this bottom-up study, we explored the German public's positive perceptions of a DGR based on a sample of N = 2,490 survey respondents in 2022. Our most compelling finding was that while some citizens viewed the resolution of the nuclear waste problem as a key benefit of a DGR, the majority either provided no positive feedback or explicitly stated that there were no benefits. Although workplaces and financial incentives are benefits recognized in existing literature, these were not prominent in our sample. Moreover, there was a clear association between the perceptions of risks and mentioned benefits: individuals who perceived high risks identified fewer positive aspects, whereas those with low-risk perception proposed more benefits. Interestingly, some respondents demonstrated ambivalence, recognizing both moderate risks and positive aspects of a DGR. Our findings indicate many people's tendency to focus on the risks associated with a DGR, overshadowing its potential benefits - a result aligning with the availability heuristic, where risks are more salient in public debate about nuclear waste. This suggests that in discussions typically framed around risks, mentioning benefits might seem inappropriate. We propose that discussing the tradeoffs between a DGR and the status quo, particularly surface storage, could broaden the conversation. Emphasizing both positive and negative aspects might shift the focus from solely on DGR risks to a more balanced view. Despite the majority of the respondents' support for DGR rather than continued surface storage, they struggled to articulate positive aspects of the solution. These inconsistencies in mental models can be expected to a certain extent, highlighting the complex nature of public risk perception and benefit recognition.