A method for data storage includes, in a system that includes one or more storage controllers, multiple servers and multiple multi-queue storage devices, assigning in each storage device server-specific queues for queuing data-path storage commands exchanged with the respective servers. At least some of the data-path storage commands are exchanged directly between the servers and the storage devices, not via the storage controllers, to be queued and executed in accordance with the corresponding server-specific queues.