Anaerobic digestion is widely used for the management of the organic fraction of municipal solid waste and is also predicted to play a vital role in the future of renewable energy production. However, reactor instability due to low acid buffering capacity at high organic loading rates in single stage reactors is a known risk of this technology. Such process instability represents a risk to electricity and heat generation through interruptions to biogas production. Co-digestion and trace element supplementation have each been advocated as strategies to stabilize biogas production, but the relative merits of these strategies have never been assessed. Here we operated a series of anaerobic continuously stirred tank reactors fed with synthetic organic household waste with or without trace element supplementation and with or without wheat straw as co-substrate at gradually increasing loading rates. Stable and high methane yields (450–550 mL/g VS) at higher organic loading rates were only maintained with trace element supplementation, regardless of co-digestion. We conclude that trace element supplementation was hierarchically more important than co-digestion at maintaining stable biogas production.