Generating mipmaps manually in GLSL

Hello, I need to generate a set of mipmaps for my texture using a custom algorithm - I need to store min values instead of average values in every subsequent level. I don't think OpenGL can do it for me automatically, so could someone please provide me with a workflow on how to do it using a shader? I can imagine it would involve some framebuffer object for binding the empty mipmapped texture and rendering into it but I don't know how to do it.. Since now I always generated mipmaps using glGenerateMipmapEXT and just accessed it in the fragment shader but have no idea how to create my own mipmaps. Thank you very much! Equilibrix