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

Light curve solutions of 12 eccentric Kepler binaries and analysis of their out-of-eclipse variability