  We consider the time delay of massive, non-relativistic, one-dimensional
particles due to a tunneling potential. In this setting the well-known Hartman
effect asserts that often the sub-ensemble of particles going through the
tunnel seems to cross the tunnel region instantaneously. An obstacle to the
utilization of this effect for getting faster signals is the exponential
damping by the tunnel, so there seems to be a trade-off between speedup and
intensity. In this paper we prove that this trade-off is never in favor of
faster signals: the probability for a signal to reach its destination before
some deadline is always reduced by the tunnel, for arbitrary incoming states,
arbitrary positive and compactly supported tunnel potentials, and arbitrary
detectors. More specifically, we show this for several different ways to define
``the same incoming state'' and ''the same detector'' when comparing the
settings with and without tunnel potential. The arrival time measurements are
expressed in the time-covariant approach, but we also allow the detection to be
a localization measurement at a later time.
