  A curious feature of quantum tunneling known as the MacColl-Hartman effect
results in the numerical observation that particles can traverse a barrier with
effective superluminal speed. However, because tunneling is never certain, any
attempt to use this effect to send a signal faster than light would require
sending many particles. In this work, we consider sending -- in parallel,
without interactions between particles -- sufficiently many particles to ensure
at the least one of them tunnels. In this case, in spite of the time advance of
the mean time for a single tunneling particle, the mean time to send one bit of
information is larger for tunneling particles than for the same number of free
photons. This removes any possibility of superluminal signaling. We show that
the mean time to send one bit using N particles is determined by the early-time
tail of the distribution of tunneling times for one particle and that, when
this early-time tail is highly accurately modeled using steepest descent, the
MacColl-Hartman effect is seen to fade away.
