  The Alperin-McKay conjecture is a longstanding open conjecture in the
representation theory of finite groups. Sp\"ath showed that the Alperin-McKay
conjecture holds if the so-called inductive Alperin-McKay (iAM) condition holds
for all finite simple groups. In a previous paper, the author has proved that
it is enough to verify the inductive condition for quasi-isolated blocks of
groups of Lie type. In this paper we show that the verification of the
iAM-condition can be further reduced in many cases to isolated blocks. As a
consequence of this we obtain a proof of the Alperin-McKay conjecture for
2-blocks of finite groups with abelian defect.
