In the study of modeling and control of continuous DTB crystallizers, it has been common practice Co assume complete dissolution of fine crystals in an external heater (fines dissolver). However, complete dissolution of fine crystals is not always guaranteed because the dissolution rate is finite. In this work, a model of an external heater is developed by taking account of the finite dissolution rate of the crystals. The model is used to study the influence of incomplete dissolution of fine crystals on the stabilizing control of the crystal size distribution (CSD). It is found to be difficult tu suppress the sustained oscillation of CSD by using the conventional SISO controllers, which regulate the amount of fines crystals by manipulating the fines flow rate, This is because when the fines flow rate is very large, an increase in the fines flow rate can reduce the amount of crystal dissolution in the external heater. It is demonstrated that instability can be avoided by imposing an upper limit on the fines flow rate. Furthermore, it is shown that the upper limit can be predicted by using the results of open-loop simulation.