  We develop infinite-dimensional Ramsey theory for Fra\"iss\'e limits of
finitely constrained free amalgamation classes in finite binary languages. We
show that our approach is optimal and in particular, recovers the exact big
Ramsey degrees proved in [2] for these structures. A crucial step in the work
develops the new notion of an A.3(2)-ideal and shows that Todorcevic's Abstract
Ramsey Theorem holds when Axiom A.3(2) is replaced by the weaker assumption of
an A.3(2)-ideal.
