Residual interaction calculations have been made for predicting the sign and the magnitude of the odd-even shifts observed in the rotational levels of theK=0 bands in the doubly-odd rare earth nuclei. It is shown that, contrary to the conclusions reached in earlier studies, the same zero-range spin-dependent residual interaction can reproduce the odd-even shifts as well as the GM splitting energies. This has been made possible with the inclusion of the phase factors for the total intrinsic spin and the total parity of the two-quasi-particle states in the Newby matrix elements. Predictions are made for the odd-even shifts for otherK=0 bands arising from several configurations not confirmed or observed so far.