  An exactly solvable bounce model in loop quantum cosmology is identified
which serves as a perturbative basis for realistic bounce scenarios. Its
bouncing solutions are derived analytically, demonstrating why recent numerical
simulations robustly led to smooth bounces under the assumption of
semiclassicality. Several effects, easily included in a perturbative analysis,
can however change this smoothness. The effective theory is not only applicable
to such situations where numerical techniques become highly involved but also
allows one to discuss conceptual issues. For instance, consequences of the
notoriously difficult physical inner product can be implemented at the
effective level. This indicates that even physical predictions from full
quantum gravity can be obtained from perturbative effective equations.
