Alpha testing is widely used for rendering surfaces with transparency. While it works well when transparency is a binary function, semi-transparent regions cause problems, as they are classified as either fully transparent or opaque. Unfortunately, semi-transparent texture regions often appear in coarser mipmap levels, causing surfaces to disappear with distance. We introduce the alpha distribution approach for pre-processing the alpha values of a texture such that alpha testing produces expected results with semi-transparency without any modification to render-time operations. We describe two separate algorithms for alpha distribution with similar qualitative behavior. Our results show that alpha distribution can produce high-quality results with low noise. We also explain how alpha distribution can be extended for high-quality rendering with alpha-to-coverage.