The innovative HB+ protocol of Juels and Weis [10] extends device authentication to low-cost RFID tags. However, despite the very simple on-tag computation there remain some practical problems with HB+ and despite an elegant proof of security against some limited active attacks, there is a simple man-in-the-middle attack due to Gilbert et al. [8]. In this paper we consider improvements to HB+ in terms of both security and practicality. We introduce a new protocol that we denote random-HB#. This proposal avoids many practical drawbacks of HB+, remains provably resistant to attacks in the model of Juels and Weis, and at the same time is provably resistant to a broader class of active attacks that includes the attack of [8]. We then describe an enhanced variant called HB# which offers practical advantages over HB+.