While the Barberis et. al (2018) model effectively captures the empirical featuresof overvaluation and high trading volume during bubbles, some empirical phenomena remain unaddressed. For example, the original model requires a shortsale constraint to generate bubbles, as fundamental traders would otherwise short too aggressively against overpricing, effectively removing the bubble. In addition, the model generates three peaks in trading volumes during a bubble which is not in accordance with the real data. The model can be made more realistic along a number of dimensions: we can allow for heterogeneous sentiment; for fundamental traders perceiving a slow correction of mispricing; and for two components to the sentiment process that drives investor demand.