A multi-film oil damper has a housing defining an annular damper cavity having an oil inlet in communication with a source of pressurized oil. A plurality of nested damper rings is disposed within the annular damper cavity, the plurality of nested damper rings defining a plurality of squeeze film annuli. Spacer rings are disposed adjacent opposed ends of the damper rings. A contact surface of the spacer rings extends radially beyond a first cylindrical surface of an associated damper ring for engaging a second cylindrical surface of an adjacent damper ring. Recesses are defined in the second cylindrical surface of the damper rings, the recesses fluidly communicating between the squeeze film annuli and the oil inlet.