In this paper, we propose an efficient, standard model, semigeneric transformation of selective-secure (hierarchical) identity-based encryption schemes into fully secure ones. The main step is a procedure that uses admissible hash functions (whose existence is implied by collision-resistant hash functions) to convert any selective-secure wildcarded identity-based encryption (WIBE) scheme into a fully secure (H)IBE scheme. Since building a selective-secureWIBE, especially with a selective-secure HIBE already in hand, is usually much less involved than directly building a fully secure HIBE, this transform already significantly simplifies the latter task. This black-box transformation easily extends to schemes secure in the continual memory leakage (CML) model of Z. Brakerski et al. [“Overcoming the hole in the bucket: Public-key cryptography resilient to continual memory leakage”. In: 51st FOCS, pp. 501–510. IEEE Computer Society Press (2010)], which allows us obtain a new fully secure IBE in that model. We furthermore show that if a selective-secure HIBE scheme satisfies a particular security notion, then it can be generically transformed into a selective-secure WIBE. We demonstrate that several current schemes already fit this new definition, while some others that do not obviously satisfy it can still be easily modified into a selective-secure WIBE.