Transformer Coupling Coefficient vs Leakage

I have a spice simulation that uses this transformer:

Turns Ration Np/Ns = 1: 278

Primary inductance = 40uH

Secondary Inductance = 3.09H

Coupling Coefficient K = 0.8 (it's a cylindrical rod core transformer)

I would like to change K to 1.0 and add external leakages so that the simulation results are the same.

This is what I tried:

Set K=1.0 Add a primary leakage of (1-K^2) * 40uH = 14.4uH Add a secondary leakage of (1-K^2) * 3.09mH = 1.11H

The results were close but not the same. So what leakage values should I use?

Jason.