We address the problem of load balancing for parallel joins. We show that the distribution of input data received and the output data produced by worker machines are both important for performance. As a result, previous work, which optimizes either for input or output, stands ineffective for load balancing. To that end, we propose a multi-stage load-balancing algorithm which considers the properties of both input and output data through sampling of the original join matrix. To do this efficiently, we propose a novel category of equi-weight histograms. To build them, we exploit state-of-the-art computational geometry algorithms for rectangle tiling. To our knowledge, we are the first to employ tiling algorithms for join load-balancing. In addition, we propose a novel, join-specialized tiling algorithm that has drastically lower time and space complexity than existing algorithms. Experiments show that our scheme outperforms state-of-the-art techniques by up to a factor of 15.