  We propose to use weak measurements away from the weak-value amplification
regime to carry out precision measurements of time delays of light. Our scheme
is robust to several sources of noise that are shown to only limit the relative
precision of the measurement. Thus, they do not set a limit on the smallest
measurable phase shift contrary to standard interferometry and weak-value based
measurement techniques. Our idea is not restricted to phase-shift measurements
and could be used to measure other small effects using a similar protocol.
