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Mesh-based applications, such as those that involve the numerical solution of partial differential equations, may be able to take advantage of the performance of computational grids. We require mesh partitioners that take the heterogeneity of the computational platform into account. Recent work in our group led to the creation of a heterogeneous mesh partitioner, PaGrid. We present a redesigned version of PaGrid, which uses estimated execution time as a cost function in all levels of multilevel refinement. It takes into account the characteristics of the application (computational complexity and size of messages) and of the computing platform (processor and network speeds), and balances the estimated execution time of processors. This results in partitions with up to 60% lower estimated execution times than METIS, a homogeneous partitioner, and similar improvements over JOSTLE, a heterogeneous partitioner. PaGrid achieves this in a reasonable amount of time, taking only two to three times longer than METIS.