Three different convective adjustment schemes are employed in the GFDL GCM to investigate if the spontaneous collapse of the thermohaline circulation under mixed boundary conditions, as observed by F. Bryan, depends on the parameterization of convective overturning. It is found that both a procedure guaranteeing complete static stability and Cox's implicit vertical diffusion scheme avoid the spontaneous collapse. Both schemes are also insensitive to the choice of time step, whereas the standard GFDL convection algorithm in conjunction with mixed boundary conditions produces results that differ qualitatively from each other when different time steps are used.