This paper extends the work of Rochester (1960) and Roden (1963) on electromagnetic coupling and its effects on length of day (lod) variations to include the effects of continuously varying mantle conductivity. Using the torque formulation of Stix (1982) and the Backus (1983) conductivity profile, an equilibrium torque Gamma-acc of 6 x 10^18 N-m and a perturbing time constant tau-c of 4 years are obtained. The tightness of coupling is increased by a factor of 7 over Rochester's model and a factor of 2.5 over Roden's best model. Perturbation torques amounting to 10-15% of the equilibrium torques now satisfactorily account for the largest changes in the lod of 3 ms/decade. This level of variability is likely since as mantle conductivity is concentrated towards the CMB (core-mantle boundary), higher harmonics become increasingly important, as is manifested in increasing low order truncation error in torque calculations. Detailed quantitative modelling must await further extension of time series and developments in measurement techniques and theory.