The original motivation for identifying codes comes from fault diagnosis in multiprocessor systems. Currently, the subject forms a topic of its own with several possible applications, for example, to sensor networks. In this paper, we concentrate on identification in binary Hamming spaces. We give a new lower bound on the cardinality of r-identifying codes when r >= 2. Moreover, by a computational method, we show that M-1 (6) = 19. It is also shown, using a non-constructive approach, that there exist asymptotically good (r, <= l)-identifying codes for fixed l >= 2. In order to construct (r, <= l)-identifying codes, we prove that a direct sum of r codes that are (l, <= l)-identifying is an (r, <= l)-identifying code for l >= 2. (C) 2007 Elsevier B.V. All rights reserved.