Cities in developing countries struggle with providing good waste collection services to all their citizens. Daily practice mostly shows low service coverage, especially in the poorer parts of cities. Up until now, research has mainly dealt with the symptoms of poor performance. This article aims at designing a qualitative System Dynamics model of the urban system that may serve as a diagnostic tool to find the root causes and leverage points for interventions. The research presented here uses a broad literature review to draw up a complex causal loop diagram describing all relevant urban variables (demographic, economic, social, financial, technical and governance-related) and their relations. The diagram is analysed using qualitative methods, partly derived from graph theory. It results in an evaluation of all variables, paths, loops and branches of the model, and finally in a simplified model. This simplified model is helpful in diagnosing waste management problems in cities, in formulating interventions and their points of leverage and even in formulating a new taxonomy that classifies cities with regard to the effect and delay in their urban processes. When it comes to interventions, the model suggests that the root cause is in populations growing faster than their economies, and that the enabling circumstances are mainly in poor governance practices that are unable to secure that tax incomes keep pace with needed budgets for sound services.