Theoretical results for spinning in the limiting cases of very small and very large applied force are obtained. The small force limit shows how the Deborah number dependence of the 'spinning viscosity', predicted for the FENE dumbbell model at low rates of strain, is due to the decay of initial stresses rather than to the extensional flow. The large force limit is consistent with expected Newtonian behaviour for fully extended dumbbells. The merit of using physically relevant quantities in the mathematical manipulation is discussed.