Anaerobic digestion (AD) is a promising option to obtain renewable energy in the form of biogas and reduce the anthropogenic impact on the environment. In recent years there has been increasing interest in using pressurized digesters to improve the quality of biogas. However, maintaining high overpressure increases the requirements for the explosion safety of digesters. Consequently, there are natural limitations in the available technologies and facilities suitable for full-scale operation. In this work, we aimed to evaluate the possibility of using overpressure in the digester to improve the efficiency of codigestion of common municipal organic waste–sewage sludge and the organic fraction of municipal solid waste. Three levels of moderate excess pressure (100, 150 and 200 kPa) were used to meet requirements of existing block-modular anaerobic bioreactors based on railway tanks, which are widely utilized for AD in the Russian Federation. There was no significant change in methane content in biogas (65% ± 3%) at different values of overpressure, hydraulic retention time (HRT) and organic loading rate (OLR). The maximum methane and energy production rates (2.365 L/(L·day) and 94.27 kJ/(L·day), respectively) were obtained at an overpressure of 200 kPa, HRT of 5 days and OLR of 14 kg VS/(m3·day). However, the maximum methane yield (202.44 mL/g VS), energy yield (8.07 kJ/g VS) and volatile solids (VS) removal (63.21%) were recorded at an overpressure of 150 kPa, HRT of 7 days and OLR of 10.4 kg VS/(m3·day). The pressured conditions showed better performance in terms of AD stability at high OLRs.