Long-term emissions of Municipal Solid Waste (MSW) landfills are a burden for future generations because of the required long-term aftercare. To shorten aftercare, treatment methods have to be developed that reduce long-term emissions. A treatment method that reduces emissions at a lysimeter scale is re-circulation of leachate. However, its effectiveness at the field scale still needs to be demonstrated. Field scale design can be improved by theoretical understanding of the processes that control the effectiveness of leachate recirculation treatment. In this study, the simplest and most fundamental sets of processes are distilled that describe the emission data measured during aerobic and anaerobic leachate recirculation in lysimeters. A toolbox is used to select essential processes with objective performance criteria produced by Bayesian statistical analysis. The controlling processes indicate that treatment efficiency is mostly affected by how homogeneously important reactants are spread through the MSW during treatment. A more homogeneous spread of i.e. oxygen or methanogens increases the total amount of carbon degraded. Biodegradable carbon removal is highest under aerobic conditions, however, the hydrolysis rate constant is lower which indicates that hydrolysis is not enhanced intrinsically in aerobic conditions. Controlling processes also indicate that nitrogen removal via sequential nitrification and denitrification is plausible under aerobic conditions as long as sufficient biodegradable carbon is present in the MSW. Major removal pathways for carbon and nitrogen are indicated which are important for monitoring treatment effectiveness at a field scale. Optimization strategies for field scale application of treatments are discussed.