Building on the emerging literature on correlation preference reflecting regret and salience considerations, we offer an axiomatization of correlation utility (CU) without requiring transitivity or completeness. Under a correlation independence axiom, CU specializes to correlation expected utility (CEU) which is not compatible with behavior in the correlated Allais common-consequence problem. This motivates our correlation betweenness axiom and characterization of the corresponding correlation betweenness utility (CBU). We investigate the implications of an absence of correlation sensitivity as well as (in)completeness for CEU and CBU. Under correlation insensitivity, we demonstrate using the Kantorovich duality that CEU reduces to EU while CBU reduces to a skew-symmetric bilinear utility together with weakening correlation independence to correlation projective independence, reducing further to weighted utility under transitivity. Finally, we characterize correlation distribution reduction preference, subsuming two major generalizations of SEU: one maintains Savage’s Postulate 2 without transitivity (Fishburn, 1989); the other maintains transitivity without Postulate 2 (Machina and Schmeidler, 1992).