A sheet offset printing method and a sheet offset printing press includes altering flow relationships in an interior of a housing of a sheet delivery of a sheet-fed printing machine to prevent uncontrolled spread of powder in the housing by extracting powder-laden air from the housing and/or feeding air into the housing from outside at a point along a return belt of a sheet conveying device. Air currents are channeled inside the housing by feeding air not laden with powder into the housing and/or leading the air into an air flow path along the return belt downstream of the point with respect to a return belt motion direction to transport the unladen air toward a printing unit by a drag effect of the return belt and/or impeding/blocking a supply of powder-charged air from around a conveyor belt of the sheet-conveyor or a powder-scattering device into a flow path along the return belt.