Hadoop is a software framework supporting the Map/Reduce programming model. It relies on the Hadoop Distributed File System (HDFS) as its primary storage system. The efficiency of HDFS is crucial for the performance of Map/Reduce applications. We substitute the original HDFS layer of Hadoop with a new, concurrency-optimized data storage layer based on the BlobSeer data management service. Thereby, the efficiency of Hadoop is significantly improved for data-intensive Map/Reduce applications, which naturally exhibit a high degree of data access concurrency. Moreover, BlobSeer's features (built-in versioning, its support for concurrent append operations) open the possibility for Hadoop to further extend its functionalities. We report on extensive experiments conducted on the Grid'5000 testbed. The results illustrate the benefits of our approach over the original HDFS-based implementation of Hadoop.