Anonymous blacklisting schemes allow online service providers to prevent future anonymous access by abusive users while preserving the privacy of all anonymous users (both abusive and non-abusive). The first scheme proposed for this purpose was Nymble, an extremely efficient scheme based only on symmetric primitives; however, Nymble relies on trusted third parties who can collude to de-anonymize users of the scheme. Two recently proposed schemes, Nymbler and Jack, reduce the trust placed in these third parties at the expense of using less-efficient asymmetric crypto primitives. We present BNymble, a scheme which matches the anonymity guarantees of Nymbler and Jack while (nearly) maintaining the efficiency of the original Nymble. The key insight of BNymble is that we can achieve the anonymity goals of these more recent schemes by replacing only the infrequent "User Registration" protocol from Nymble with asymmetric primitives. We prove the security of BNymble, and report on its efficiency.