By combining techniques of watermarking and fingerprinting, a sound buyer-seller watermarking protocol can address the issue of copyright protection in e-commerce. In this paper, we analyze the security of two recent anonymous buyer-seller watermarking protocols proposed by Ju et. al and Choi et. al respectively, and prove that they do not provide the features and security as claimed. In particular, we show that i) the commutative cryptosystem used in Choi et. als protocol fails to prevent the watermark certification authority (WCA) from discovering the watermark (fingerprint) chosen by the buyer; ii) for both protocols, the seller can discover the watermark chosen by the buyer if he colludes with the WCA. Hence, these protocols cannot guard against conspiracy attacks. We further show that these protocols only provide partial anonymity, ie. the buyers anonymity is guaranteed only if WCA is honest. Our results suggest that the security of these protocols must assume the honesty of WCA, contrary to the designers original claim. Finally, we propose a new anonymous buyer-seller watermarking protocol which is more secure and efficient, and provides true anonymity.