  Precision measurements of ultra-small linear velocities of one of the mirrors
in a Michelson interferometer are performed using two different weak-values
techniques. We show that the technique of Almost-Balanced Weak Values (ABWV)
offers practical advantages over the technique of Weak-Value Amplification
(WVA), resulting in larger signal-to-noise ratios and the possibility of longer
integration times due to robustness to slow drifts. As an example of the
performance of the ABWV protocol we report a velocity sensitivity of 60 fm/s
after 40 hours of integration time. The sensitivity of the Doppler shift due to
the moving mirror is of 150 nHz.
