A population balance equation for a CST crystallizer with agglomeration and an exponential crystal distribution in the feed is solved analytically. A solution to the crystal free feed case is also obtained as a special case, and matches with that given by Liao and Hulburt (1976, Annual Meeting of AIChE). For the crystal free feed case, it is proved that a unimodal distribution is only predicted, which is in agreement with the analysis of Lui and Thompson (1992, Chem. Engng Sci. 47, 1897-1901). Comparison with the exponential distribution, after transforming both distributions using the same dimensionless variables, shows that, for certain values of the parameters, narrow distributions of small-sized particles are observed. A different choice of dimensionless variables which is more natural to investigate the effect of agglomeration is also pointed out.