Custom downsampler for 3D texture

I have a 3D texture I need to downsample all the way down the mipchain, but a linear filter will not suffice. I need some very specific logic to handle the pixel blending. I was wondering if a compute shader is the right route to go for this, so I can compute the entire mipchain all in one go? I have not used these before, any thoughts on this?

Makes sense to me. Not that you have much choice, if LINEAR or NEAR is not good enough for you. It is either Compute shader, or compute-like fragment shader.

Well, the alternative is to render to the 3D texture one slice at a time. Which is why I am wondering, does a compute shader offer any advantage in this situation?