Abstract: Flue gases from fuel-fired appliances such as household gas furnaces contain water vapor which may form condensate on the walls of the external flue pipe leading from the appliance. The present invention provides a special flue pipe connection between the internal flue pipe and the external flue pipe. The connection accepts the lower end of the external flue pipe, directs condensate moving down the walls of the external flue pipe to a condensate drain outlet provided in the connection and passes flue gases from the internal flue pipe upwardly into the external flue pipe while isolating those gases from the condensate being drained. In the preferred construction the connection is a collar having an upwardly facing cylindrical recess into which the lower end of the external flue pipe fits and, within the recess, a short pipe section having a lower end connectable to the internal flue pipe and an upper end through which flue gases pass into the external flue pipe.