Surprising noun order involving the の particle


I am puzzled by the word ordering in the following sentence:

> そのうちの一つの[箱]{はこ}は私のです。

This sounds unnatural to me, though I was told that this is correct by a
native speaker (who was not able to explain why). Whenever I've encountered
this linking/nominalization/possessive particle before, the nouns were ordered
with increasing specificity. (e.g. 友達の本の名前).

Based on that principle, I would have expected the sentence to read

> その[箱]{はこ}のうちの一つは私のです。

I.e.:

  1. most general: 箱 (box(es)),
  2. more specific 箱のうち (amongst the boxes)
  3. most specific: 箱のうちの一つ (one of the boxes)

What am I missing?




If I'm not mistaken, I think there are two acceptable ways to say this in
English, too:

> そのうちの一つの箱は私のです。  
>  One box among those is mine. (more literally) Among those, one box is mine.
>
> その箱のうちの一つは私のです。  
>  One of those boxes is mine.

It's true the former looks slightly less-organized, but the nuance is fairly
small in spoken language.




If I'm not mistaken, I think there are two acceptable ways to say this in
English, too:

> そのうちの一つの箱は私のです。  
>  One box among those is mine. (more literally) Among those, one box is mine.
>
> その箱のうちの一つは私のです。  
>  One of those boxes is mine.

It's true the former looks slightly less-organized, but the nuance is fairly
small in spoken language.

