  Single-particle dispersion in the Bolgiano--Obukhov regime of two-dimensional
turbulent convection is investigated. Unlike dispersion in a flow displaying
the classical K41 phenomenology, here, the leading contribution to the
Lagrangian velocity fluctuations is given by the largest eddies. This implies a
linear behavior in time for a typical velocity fluctuation in the time interval
$t$. The contribution to the Lagrangian velocity fluctuations of local eddies
(i.e. with a characteristic time of order $t$), whose space/time scalings are
ruled by the Bolgiano--Obukhov theory, is thus not detectable by standard
Lagrangian statistical observables. To disentangle contributions arising from
the large eddies from those of local eddies, a strategy based on exit-time
statistics has successfully been exploited. Lagrangian velocity increments in
Bolgiano convection thus provide a physically relevant example of signal with
\emph{more than smooth} fluctuations.
