In a recent paper, Al-Sarkhi and Hanratty examined the influence of a drag-reducing polymer on air-water annular flows in a 9.53 cm pipeline. This paper describes similar studies in a 2.54 cm pipe, for which the annular flow has different characteristics and for which the friction factors assume larger values in air-water systems. Both studies show a maximum drag reduction that is accompanied (in most cases) by a change to a stratified flow for which the concentration of drops in the gas phase is zero or close to zero, and for which the friction factor is about 1.5 times what would be observed for air flowing alone. The amount of drag reduction, therefore, depends on the magnitude of the friction factor for the air-water flow. Drag reductions up to 63% were observed in the 2.54 cm pipe. This is to be compared with the 48% previously achieved in the 9.54 cm pipe. Larger concentrations of polymer are needed to obtain maximum drag reduction in the smaller pipe.