  The eccentricity, periastron angle, orbital inclination, mass ratio, stellar
temperatures and relative stellar radii of 12 eclipsing eccentric binaries were
determined on the basis of Kepler data. The analysis of their out-of-eclipse
variability led to the following results: (i) KIC 10490980 exhibits rotational
(spot-type) variability; (ii) Four new heartbeat stars were found: KIC 9344623
and KIC 10296163, which have wide tidally induced light humps and KIC 9119405
and KIC 9673173, which have narrow "W-shape" features; (iii) KIC 4932691 shows
oscillations with approximately the 18th harmonic of the orbital period. We
established that the eccentric Kepler binaries fall below the envelope
P(1-e^2)^{3/2} = 5 days on the period-eccentricity diagram and that there is a
surprising lack of eccentric binaries with periods of 25-35 days.
