Much of the lore of the Zitterbewegung of a free Dirac particle is found to need revision for the situation when the particle is initially localized. We find that in this case the rapid violent oscillations of angular frequency ∠2mc2/h□ in the average position of the particle are a transient rather than sustained phenomenon. Instead, the Zitterbewegung is manifested by a growth in the size of the particle but this growth is many orders of magnitude smaller than h□/mc, the magnitude usually quoted. This behavior is contrasted with that of the Foldy-Wouthuysen position for which the Zitterbewegung is absent. Finally, the applicability of these ideas to the situation of a localized Dirac particle in an external field is commented on.