Data caches are essential in modern processors, bridging the widening gap between main memory and processor speeds. However, they yield very complex performance models, which makes it hard to bound execution times tightly. This paper contributes a new technique to obtain predictability in preemptive multitasking systems in the presence of data caches. We explore the use of cache partitioning, dynamic cache locking and static cache analysis to provide worst-case performance estimates in a safe and tight way. Cache partitioning divides the cache among tasks to eliminate inter-task cache interferences. We combine static cache analysis and cache locking mechanisms to ensure that all intra-task conflicts, and consequently, memory access times, are exactly predictable. To minimize the performance degradation due to cache partitioning and locking, two strategies are employed. First, the cache is loaded with data likely to be accessed so that their cache utilization is maximized. Second, compiler optimizations such as tiling and padding are applied in order to reduce cache replacement misses. Experimental results show that this scheme is fully predictable, without compromising the performance of the transformed programs. Our method outperforms static cache locking for all analyzed task sets under various cache architectures, with a CPU utilization reduction ranging between 3.8 and 20.0 times for a high performance system.