Abstract We study the existential closures of several propositional languages L considered recently as target languages for knowledge compilation (KC), namely the incomplete fragments KROM-C, HORN-C, K/H-C, renH-C, AFF, and the corresponding disjunction closures KROM-C[?], HORN-C[?], K/H-C[?], renH-C[?], and AFF[?]. We analyze the queries, transformations, expressiveness and succinctness of the resulting languages L[?] in order to locate them in the KC map. As a by-product, we also address several issues concerning disjunction closures that were left open so far. From our investigation, the language HORN ? C[?, ?] (where disjunctions and existential quanti?cations can be applied to Horn CNF formulae) appears as an interesting target language for the KC purpose, challenging the in?uential DNNF languages.