FASTEST-3D is an MPI-parallel finite-volume flow solver based on block-structured meshes that has been developed at the University of Erlangen-Nuremberg since the early 1990s. It can be used to solve the laminar or turbulent incompressible Navier-Stokes equations. Up to now its scalability was strongly limited by a rather rigid communication infrastructure, which led to a dominance of MPI time already at small process counts. This paper describes several optimizations to increase the performance, scalability, and flexibility of FASTEST-3D. First, a node-level performance analysis is carried out in order to pinpoint the main bottlenecks and identify sweet spots for energy-efficient execution. In addition, a single-precision version of the solver for the linear equation system arising from the discretization of the governing equations is devised, which significantly increases the single-core performance. Then the communication mechanisms in FASTEST-3D are analyzed and a new communication strategy based on non-blocking calls is implemented. Performance results with the revised version show significantly increased single-node performance and considerably improved communication patterns along with much better parallel scalability. In this context we discuss the concept of "acceptable parallel efficiency" and how it influences the real gain of the optimizations. Scaling measurements are carried out on a modern petascale system. The obtained improvements are of major importance for the use of FASTEST-3D on current high-performance computer clusters and will help to perform simulations with much higher spatial and temporal resolution to tackle turbulent flow in technical applications.