Slip velocity is measured in straight-walled capillary dies and semihyperbolically converging dies (SHCDs) in three industrial polymer melts, with and without the presence of a viscosity reducing stearic acid (SA) additive. Data taken in shear flow through capillary dies indicated a substantial increase in the slip velocity caused by the addition of the SA. Data taken in the SHCDs showed much less of an increase in the slip velocity of the polymer/additive system relevant to the neat polymer. One possible explanation of this observation is that the magnitude of the slip velocity is directly related to the degree of orientation within the flowing polymeric material.