A three-box model of the Atlantic Ocean is used to examine the in?uence different parameterisations of the diapycnal mixing may have on the large scale dynamics of the ocean circulation. Special emphasis is given to the northward volume and heat transports. The vertical diffusivity k is taken in the general form k~N^(-alpha), where N is the buoyancy frequency, and the parameter space 0<alpha<3 is explored. An imposed freshwater forcing of the northern high latitude box is used as a test case to investigate the behaviour of the model compared to similar types of sensitivity experiments carried out with, for instance, General Circulation Models. Four different solution states are identi?ed, separated by three critical values of alpha. For small values of alpha, both heat and volume ?uxes decrease with increasing freshwater ?ux. Increasing a leads ?rst into a parameter domain where the transport of heat increases with increasing freshwater forcing, then at even higher alpha also the volume transport increases. Finally, a fourth state is found where strong advection of warm water leads to an increase of the northern box temperature, as opposed to cooling for small alpha. The behaviour of the critical values of a is discussed with respect to model dynamics and parameters. A subtle interplay between changes in the thermocline depth and the advective ?uxes from the thermocline box into northern box, which both are modulated by diapycnal mixing, is found to be the key process in determining the behaviour of the model. Finally, the implications for modelling and understanding of basic features of the ocean circulation are discussed.