In this work the nature of confinement improvement implied by the self-consistent generation of mean flows in two-dimensional convective turbulence is studied. The confinement variations are linked to two distinct regulation mechanisms which are also shown to be at the origin of low-frequency bursting in the fluctuation level and the convective heat flux integral, both resulting in a state of large-scale intermittency. The first one involves the control of convective transport by sheared mean flows. This regulation relies on the conservative transfer of kinetic energy from tilted fluctuations to the mean component of the flow. Bursting can also result from the quasi-linear modification of the linear instability drive which is the mean pressure gradient. For each bursting process the relevant zero-dimensional model equations are given. These are finally coupled in a minimal model of convection in fluids and plasmas. The results of the modeling are used to discuss confinement scaling and intermittency, and in a heuristic way, more complex issues such as criticality and transport avalanches. (C) 2003 American Institute of Physics.