  Transit times around single stars can be described well by a linear
ephemeris. However, transit times in circumbinary systems are influenced both
by the gravitational perturbations and the orbital phase variations of the
central binary star. Adopting a coplanar analog of Kepler-16 as an example, we
find that circumbinary planets can transit the same star more than once during
a single planetary orbit, a phenomenon we call "tight transits". In certain
geometric, the projected orbital velocity of the planet and the secondary star
can approach zero and change sign, resulting in very long transits and/or 2-3
transits during a single binary orbit. Whether tight transits are possible for
a particular system depends primarily on the binary mass ratio and the orbital
architecture of both the binary and the planet. We derive a time-dependent
criterion to judge when tight transits are possible for any circumbinary
system. These results are verified with full dynamical integrations that also
reveal other tight transit characteristics, i.e., the transit durations and the
intervals between tight transits. For the seven currently known circumbinary
systems, we estimate these critical parameters both analytically and
numerically. Due to the mutual inclination between the planet and the binary,
tight transits can only occur across the less massive star B in Kepler-16, -34,
-35, and -47 (for both planets). The long-term average frequency of tight
transits (compared to typical transits) for Kepler-16, -34, and -35 are
estimated to be several percent. Using full numerical integrations, the next
tight transit for each system is predicted and the soonest example appears to
be Kepler-47b and -47c, which are likely to have tight transits before 2025.
These unique and valuable events often deserve special observational scrutiny.
