  We investigate the disturbance of the state of a quantum system in a
protective measurement for finite measurement times and different choices of
the time-dependent system-apparatus coupling function. The ability to minimize
this state disturbance is essential to protective measurement. We show that for
a coupling strength that remains constant during the measurement interaction of
duration $T$, the state disturbance scales as $T^{-2}$, while a simple
smoothing of the coupling function significantly improves the scaling behavior
to $T^{-6}$. We also prove that the shift of the apparatus pointer in the
course of a protective measurement is independent of the particular time
dependence of the coupling function, suggesting that the guiding principle for
choosing the coupling function should be the minimization of the state
disturbance. Our results illuminate the dynamics of protective measurement
under realistic circumstances and may aid in the experimental realization of
such measurements.
