  We discuss the Quantum-Koszul method for constructing star products on
reduced phase spaces in the symplectic, regular case. It is shown that the
reduction method proposed by Kowalzig, Neumaier and Pflaum for cotangent
bundles is a special case of the Quantum-Koszul method. We give sufficient
conditions that reduction by stages is possible in the Quantum-Koszul framework
and show that the star product obtained by two steps is identical to that
obtained by one step. In order to do so, we prove an equivariant version of the
compatible tubular neighborhood theorem.
