Organic solid waste is pressed at a high pressure to separate the solid waste into a dry fraction and a wet fraction. The wet fraction is diluted and floatables (i.e. pieces of plastic and/or paper) in the wet fraction are comminuted. The wet fraction is then de-gritted before being sent to an anaerobic digester. Digestate is withdrawn from the digester from a free liquid surface of the digester. The digestate is filtered to extract comminuted floatables. The resulting filtrate is then composted or directly applied to land. A corresponding system comprises a press, a grinder, a hydrocyclone, an anaerobic digester, a filter and a dewaterer.