Abstract. A not well-known result [9, Theorem 4.4] in formal language theory is that the Higman-Haines sets for any language are regular, but it is easily seen that these sets cannot be effectively computed in general. Here the Higman-Haines sets are the languages of all scattered subwords of a given language and the sets of all words that contain some word of a given language as a scattered subword. Recently, the exact level of unsolvability of Higman-Haines sets was studied in [10]. We focus on language families whose Higman-Haines sets are effectively constructible. In particular, we study the size of Higman-Haines sets for the lower classes of the Chomsky hierarchy, namely for the families of regular, linear contextfree, and context-free languages, and prove upper and lower bounds on the size of these sets. 1