  We revisit the approaches to the solution of parity games based on progress
measures and show how the notion of quasi dominions can be integrated with
those approaches. The idea is that, while progress measure based techniques
typically focus on one of the two players, little information is gathered on
the other player during the solution process. Adding quasi dominions provides
additional information on this player that can be leveraged to greatly
accelerate convergence to a progress measure. To accommodate quasi dominions,
however, non trivial refinements of the approach are necessary. In particular,
we need to introduce a novel notion of measure and a new method to prove
correctness of the resulting solution technique.
