I think this is a case where gentoo can really shine. Although tooling might not be there just yet, the linux meta distribution allows you to build a strict set of dependencies based on what you need and nothing else. There's already been pretty successful attempts at this, such as https://github.com/edannenberg/gentoo-bb (63mb custom nginx sound ok to you?) or https://github.com/wking/dockerfile.

edit: To elaborate for people not very familiar with gentoo; it solves what a lot of the discussion in this thread seems to be about - having complete control of the dependency chain based on how you choose to build your software. Using nginx as an example, enabling mod_security would pull and build its own dependencies (which also can be limited based on its compiler options). Strip man pages? Done. Change libc library? No problem (if the packages support it).

The work that needs to be done is expanding the toolset to a point where you say "I want this in docker, plx" and anything else (dependencies disregarded) basically goes out the window. The current attempts builds upon a small set of packages for convenience then removes "safe" stuff. When time allows, I'd like to be much more aggressive in terms of what's considered safe. :edit

I'm personally also very interested in progrium's work with bundling busybox with opkg (https://github.com/progrium/busybox), but still think that docker containers should not be built from within - which why cross compiling from gentoo to create a minimal docker image is the way to go.