Use case sensitive search for lower-case string using smartcase

I normally enable smartcase in my .vimrc.

Without smartcase:

• If I want case-insensitive search, I write in upper-case or lower-case (doesn't matter) and append a \c at the end of the query.
• Case-sensitive search happens by default.

With smartcase:

• If I want case insensitive search, I write all in lower-case.
• If I want case sensitive search, I write the upper-case letters in upper-case.

But, with smartcase enabled, how can I say that I want a case sensitive search of a lower-case pattern? I was expecting that appending a \c would revert the type of search (so that if I had written all in lower-case, i.e. case-insensitive search, it would turn to a case-sensitive search; and if I had written some upper-case letters, i.e. case-sensitive search, it would turn to a case-insensitive search), but that does not seem to be the case (no pun intended).