  We prove a generic completeness result for a class of modal fixpoint logics
corresponding to flat fragments of the two-way mu-calculus, extending earlier
work by Santocanale and Venema. We observe that Santocanale and Venema's proof
that least fixpoints in the Lindenbaum-Tarski algebra of certain flat fixpoint
logics are constructive, using finitary adjoints, no longer works when the
converse modality is introduced. Instead, our completeness proof directly
constructs a model for a consistent formula, using the induction rule in a way
that is similar to the standard completeness proof for propositional dynamic
logic. This approach is combined with the concept of a focus, which has
previously been used in tableau based reasoning for modal fixpoint logics.
