  We study entanglement dynamics in a diagonal dephasing model in which the
strength of interaction decays exponentially with distance -- the so-called
l-bit model of many-body localization. We calculate the exact expression for
entanglement growth with time, finding in addition to a logarithmic growth, a
sublogarithmic correction. Provided the l-bit picture correctly describes the
many-body localized phase this implies that the entanglement in such systems
does not grow (just) as a logarithm of time, as believed so far.
