national sovereignty--a vacuous concept?

So whenever we talk about intervention in another country for humanitarian reasons, there are generally two ideas that we pull out of our heads: the humanitarian concept (that there are some situations that demand us, as human beings, to respond) and the notion of national sovereignty (that whatever goes on in another country is their own business). These two, in theory, pull at each other in a roughly equivalent way, and we generally try to find the balance between them when dealing with world hotspots.

Except I'm not sure we actually do. The two claims are certainly not equal--the former is a moral imperative, the latter a rational construct--and humanitarianism is clearly the prior concern. Additionally, sovereignty can be negatively defined in a way humanitarianism just can't:

*sovereignty is just what we call it when the conditions demanding humanitarian intervention don't obtain (that is, the number of people involved is small, or violence is not occurring/is not sufficiently widespread)
*humanitarianism is just what we call it when the conditions for sovereignty don't obtain

the second doesn't work because the second part of the thought requires that either a. there be no coercive state power (intervention might be humanitarian then, but it isn't clearly so) or b. the claims the rulers of a particular nation aren't valid because they violate natural law or something similar--but this requires exactly the sort of notion that underlies the humanitarian concept.

Anyway, I've been trying to think of examples lately where sovereignty qua sovereignty is the explanation for not intervening in a particular problem, where saying that the conditions for humanitarianism don't obtain is not an equally good explanation. I'm convinced at least part of the reason I'm having this problem is because the idea of sovereignty might just be gibberish.

But then again, maybe I'm wrong.