Within the last few years, a countless number of blockchain systems have emerged on the market, each one claiming to revolutionize the way of distributed transaction processing in one way or the other. Many blockchain features, such as byzantine fault tolerance, are indeed valuable additions in modern environments. However, despite all the hype around the technology, many of the challenges that blockchain systems have to face are fundamental transaction management problems. These are largely shared with traditional database systems, which have been around for decades already. These similarities become especially visible for systems, that blur the lines between blockchain systems and classical database systems. A great example of this is Hyperledger Fabric, an open-source permissioned blockchain system under development by IBM. By implementing parallel transaction processing, Fabric's workflow is highly motivated by optimistic concurrency control mechanisms in classical database systems. This raises two questions: (1)~Which conceptual similarities and differences do actually exist between a system such as Fabric and a classical distributed database system? (2)~Is it possible to improve on the performance of Fabric by transitioning technology from the database world to blockchains and thus blurring the lines between these two types of systems even further? To tackle these questions, we first explore Fabric from the perspective of database research, where we observe weaknesses in the transaction pipeline. We then solve these issues by transitioning well-understood database concepts to Fabric, namely transaction reordering as well as early transaction abort. Our experimental evaluation under the Smallbank benchmark as well as under a custom workload shows that our improved version Fabric++ significantly increases the throughput of successful transactions over the vanilla version by up to a factor of 12x, while decreasing the average latency to almost half.