The most popular framework that fits this description might be Pyramid [1].

[1]: https://trypyramid.com/

Have you looked at: http://www.django-rest-framework.org/

and the Lightweight Django book: http://shop.oreilly.com/product/0636920032502.do

I like to keep things modular, if you're looking for API development Falcon is a lightweight DIY solution (https://falconframework.org/).

Use Django and strip out the middleware and admin/authentication addons.

see https://github.com/lightweightdjango

auth is a must-have (i've never written an app that did not need basic auth) and admin is a very, very nice to have. It still feels "thick" to me in other areas.

Agreed! I lean much more towards Flask (I'd rather have too much simplicity than too much complexity), but something in the middle would be fantastic.

A simple application structure with loose enough rules and a strong standard library is what I would like. Flask can be too little, Django can be too big.

Pyramid is exactly that.