Keeping in mind that every situation (as every child) is unique, what worked well for us was that our daughter's skips were separated by three years (she skipped 2nd and 6th grades).
The first acceleration was a complete no-brainer as she should have gone to K a year ahead of when she was allowed to. Unfortunately the first school my daughter went to viewed grade skipping as a form of child abuse.
The decision for the second skip was made after seeing how well she adapted to the first skip. Her test scores took a slight dip (percentile) in the first year, but were back at the top of her grade by the next year. That, plus how well she fit in with her older classmates help make the decision for another skip easier.
One comment I remember from the IAS meeting for the second acceleration, was from one of the teachers on the committee who my daughter had spent a day with. The teacher commented that she did not know my daughter had already been accelerated once because she fit in so well with the other kids.
