Stencil computations are not well optimized by general-purpose production compilers and the increased use of multicore, manycore, and accelerator-based systems makes the optimization problem even more challenging. In this paper we present Snowflake, a Domain Specific Language (DSL) for stencils that uses a "micro-compiler" approach, i.e., small, focused, domain-specific code generators. The approach is similar to that used in image processing stencils, but Snowflake handles the much more complex stencils that arise in scientific computing, including complex boundary conditions, higherorder operators (larger stencils), higher dimensions, variable coefficients, non-unit-stride iteration spaces, and multiple input or output meshes. Snowflake is embedded in the Python language, allowing it to interoperate with popular scientific tools like SciPy and iPython; it also takes advantage of built-in Python libraries for powerful dependence analysis as part of a just-in-time compiler. We demonstrate the power of the Snowflake language and the micro-compiler approach with a complex scientific benchmark, HPGMG, that exercises the generality of stencil support in Snowflake. By generating OpenMP comparable to, and OpenCL within a factor of 2× of hand-optimized HPGMG, Snowflake demonstrates that a micro-compiler can support diverse processor architectures and is performance-competitive whilst preserving a high-level Python implementation.