to fit in her purse

Which are correct:

1) She had a handgun to fit in her purse.

2) She had a small handgun to fit in her purse.

3) She bought a handgun to fit in her purse.

4) She bought a small handgun to fit in her purse.

I was wondering if the adjective (small) was necessary here. I think without it the sentences don't sound natural, but I am not sure.

Gratefully

Navi