Instruction selection is a well-studied compiler phase that translates the compiler's intermediate representation of programs to a sequence of target-dependent machine instructions optimizing for various compiler objectives ( e.g. speed and space). Most existing instruction selection techniques are limited to the scope of a single statement or a basic block and cannot cope with irregular instruction sets that are frequently found in embedded systems. We consider an optimal technique for instruction selection that uses Static Single Assignment ( SSA ) graphs as an intermediate representation of programs and employs the Partitioned Boolean Quadratic Problem ( PBQP ) for finding an optimal instruction selection. While existing approaches are limited to instruction patterns that can be expressed in a simple tree structure, we consider complex patterns producing multiple results at the same time including pre/post increment addressing modes, div-mod instructions, and SIMD extensions frequently found in embedded systems. Although both instruction selection on SSA-graphs and PBQP are known to be NP-complete, the problem can be solved efficiently - even for very large instances. Our approach has been implemented in LLVM for an embedded ARMv5 architecture. Extensive experiments show speedups of up to 57% on typical DSP kernels and up to 10% on SPECINT 2000 and MiBench benchmarks. All of the test programs could be compiled within less than half a minute using a heuristic PBQP solver that solves 99.83% of all instances optimally.