We study various shortcut fusion rules for languages like Haskell. Following a careful semantic account of a recently proposed rule for circular program transformation, we propose a new rule that trades circularity for higher-orderedness, and thus attains better semantic properties. This also leads us to revisit the original foldr/build-rule, as well as its dual, and to develop variants that do not suffer from detrimental impacts of Haskell’s mixed strict/nonstrict semantics. Throughout, we offer pragmatic insights about our new rules to investigate also their relative effectiveness, rather than just their semantic correctness.