  A Petri net is choice-free if any place has at most one transition in its
postset (consuming its tokens) and it is (extended) free-choice (EFC) if the
postsets of any two places are either equal or disjoint. Asymmetric choice (AC)
extends EFC such that two places may also have postsets where one is contained
in the other. In reduced AC nets this containment is limited: If the postsets
are neither disjoint nor equal, one is a singleton and the other has exactly
two transitions. The aim of Petri net synthesis is to find an unlabelled Petri
net in some target class with a reachability graph isomorphic to a given finite
labelled transition system (lts). Choice-free nets have strong properties,
allowing to often easily detect when synthesis will fail or at least to quicken
the synthesis. With EFC as the target class, only few properties can be checked
ahead and there seem to be no short cuts lowering the complexity of the
synthesis (compared to arbitrary Petri nets). For AC nets no synthesis
procedure is known at all. We show here how synthesis to a superclass of
reduced AC nets (not containing the full AC net class) can be done.
