A tip for Japanese learners. How to use "口が軽い"

Do you have anyone around you who easily tells others' secrets? They sometimes may be troublesome. You call them "口が軽い人" in Japanese and it's an adjective to describe such people. You can think it's almost same as someone who has a big mouth. I give an example.

「なんでみんなあのこと知ってるの！？」
「実は彼に言っちゃった・・・。」
「あいつ口軽いから、あいつには言ったらだめだって！」
"How come everyone knows that thing!?"
"Actually... I told to him."
"You shouldn't tell him! He has a big mouth."

On the contrary, what do you call people who can keep a secret in Japanese?
Some people may guess it's "口が重い" since the opposite word of "軽い" is "重い", but they are figurative phrases and the answer is "口がかたい." I don't know a figurative phrases referring to "口がかたい" like "big mouth" for "口が軽い." Is there a good phrase in English?

In association with these, there's a saying of "口は災いの元(kuti ga wazawai no moto)" , which means you cause troubles when you easily tell others' secret, so be careful.

I googled big mouth and searched for good ralate related pictures to put on this journal, but I gave up because only creepy pictures only were on (ただこの言い方がちょっと変と思います(T_T)).

I hope you'll visit read(may sounds more acurate^^) my journals. Bye!