We present a method to create high-quality sampling filters by combining a prescribed number of texels from several resolutions in a mipmap. Our technique provides fine control over the number of texels we read per texture sample so that we can scale quality to match a memory bandwidth budget. Our method also has a fixed cost regardless of the filter we approximate, which makes it feasible to approximate higher-quality filters such as a Lánczos 2 filter in real-time rendering. To find the best set of texels to represent a given sampling filter and what weights to assign those texels, we perform a cardinality-constrained least-squares optimization of the most likely candidate solutions and encode the results of the optimization in a small table that is easily stored on the GPU. We present results that show we accurately reproduce filters using few texel reads and that both quality and speed scale smoothly with available bandwidth. When using four or more texels per sample, our image quality exceeds that of trilinear interpolation.