The latest trend towards performance asymmetry among cores on a single chip of a multicore processor is posing new software engineering challenges for developers. A key challenge is that for effective utilization of these performance-asymmetric multicore processors, code sections of a program must be assigned to cores such that the resource needs of a section closely matches resource availability at the assigned core. Determining this assignment manually is tedious, error prone, and it significantly complicates software development. We contribute a transparent and fully-automatic program analysis, which we call phase-based tuning, to solve this problem. Phase-based tuning adapts an application to effectively utilize performance-asymmetric cores of a processor. Our technique does not require any changes in the compiler or operating system, thus it is easy to deploy in existing tool chains. It does not require any input from the programmer except the application. Furthermore, it is independent of the characteristics (performance-asymmetry) of the target multicore processor, which has two benefits. First, it avoids the need to create multiple customizations of the binary for each target architecture, and second it relieves the programmer of the burden of anticipating the target architecture. Last but not least, our technique significantly improves performance. Compared to the stock Linux scheduler, our best technique shows 36% average process speedup, while maintaining fairness and with negligible overheads.