  We employ a recently developed methodology -- called "structural refinement"
-- to extract nested sequent systems for a sizable class of intuitionistic
modal logics from their respective labelled sequent systems. This method can be
seen as a means by which labelled sequent systems can be transformed into
nested sequent systems through the introduction of propagation rules and the
elimination of structural rules, followed by a notational translation. The
nested systems we obtain incorporate propagation rules that are parameterized
with formal grammars, and which encode certain frame conditions expressible as
first-order Horn formulae that correspond to a subclass of the Scott-Lemmon
axioms. We show that our nested systems are sound, cut-free complete, and admit
hp-admissibility of typical structural rules.
