There is a lot of talk about it and the conclusion is that there is no need to take action.

The estimated max is 11 billion because the birthrate is very low right now.

The 'problem' is that we live longer.

In many developed countries the population is decreasing.

Do ethical strategies to accomplish that exist?

Sure, depends only on your ethic. E.G (note devils advocate) A utilitarist might argue, that killing of a larger amount of humans that are not worth it might be for the greater good of all

A extremist fascist even has a pretty clear definition of worth added to that

Asimovs concept of being killed instead of retirement

Various concepts in fiction of adding globally some additions to drinking water to lower fertility on global scale

Chinas politic of one child per family was even somewhat fair as it discriminates equally

You mean the Sixty in time enough for love - don't think he was propsing it as a good thing