Recent research has demonstrated the multidimensional nature of poverty and the multi-level organization of social-ecological systems that display poverty traps. The traps on these different levels can reinforce each other, and therefore multi-level traps pose particular challenges for poverty alleviation. Yet, poverty trap models rarely consider more than one level of organization and only a few attributes of the system at each level. These limitations constrain our understanding of the mechanisms that generate poverty traps and may hinder or even mislead development efforts. Here, we present a series of two-level dynamical system models of poverty traps and use these models to investigate the combined influences of biophysical and economic factors, farmers’ habits and community decisions on creating and alleviating persistent poverty. Our results indicate that neglecting key interactions can lead to incorrect assessments and potentially inadequate alleviation strategies. Moreover, we obtain necessary conditions for the existence of fractal poverty traps, and show that (i) cross-level interactions can open possibilities for escaping from poverty, (ii) that farmers’ behavioral changes may create or impede a way out of poverty, and (iii) that the effectiveness of development interventions depends on the combined influences of biophysical and economic dynamics, farmers’ behavior and community spending on agricultural and social activities.