The variance stabilizing transformations formally introduced by Bartlett (1947) are often seen to also approximately normalize the random variable. This is not due to the variance stabilizing proerty, but because these transformations often induce symmtery. In this note, we obtain a condition under which the varianc stabilizing transformation is also an approximately symmetrizing transformation and examine some familiar transformations in this light. We also construct a differential equation, analogous to Bartlett's for obtaing an approximately symmetrizing transformation and illusrtate it in terms of common cases.