Bitcoin, the arguably most popular cryptocurrency to date, allows users to perform transactions using freely chosen pseudonymous addresses. Previous research, however, suggests that these pseudonyms can easily be linked, implying a lower level of privacy than originally expected. To obfuscate the links between pseudonyms, different mixing methods have been proposed. One of the first approaches is the CoinJoin concept, where multiple users merge their transactions into one larger transaction. In theory, CoinJoin can be used to mix and transact bitcoins simultaneously, in one step. Yet, it is expected that differing bitcoin amounts would allow an attacker to derive the original single transactions. Solutions based on CoinJoin therefore prescribe the use of fixed bitcoin amounts and cannot be used to perform arbitrary transactions.In this paper, we define a model for CoinJoin transactions and metrics that allow conclusions about the provided anonymity. We generate and analyze CoinJoin transactions and show that with differing, representative amounts they generally do not provide any significant anonymity gains. As a solution to this problem, we present an output splitting approach that introduces sufficient ambiguity to effectively prevent linking in CoinJoin transactions. Furthermore, we discuss how this approach could be used in Bitcoin today.