Miley Cyrus in tit-for-tat exchange with Sinead O'Connor

Former Disney teen idol turned bad-girl pop star Miley Cyrus hit back Thursday at Sinead O'Connor, rebuffing advice by the Irish singer that she stop prostituting herself for music business bosses.

Cyrus, in the headlines repeatedly since her infamous twerking performance at the MTV Video Music Awards show in August, fired off a couple of tweets to O'Connor evoking mental health problems.

The tit-for-tat episode started with a cover story interview Cyrus gave in the latest issue of Rolling Stone, in which she revealed that her latest video for "Wrecking Ball" was inspired by O'Connor's "Nothing Compares 2 U."

In the video, the 20-year-old former "Hannah Montana" star swings on a huge demolition ball -- naked except for chunky boots and a come-hither smile.

In a blog on O'Connor's website, the Irish singer wrote: "I am extremely concerned for you that those around you have led you to believe, or encouraged you in your own belief, that it is in any way 'cool' to be naked and licking sledgehammers in your videos.

"It is in fact the case that you will obscure your talent by allowing yourself to be pimped, whether its the music business or yourself doing the pimping.

"Nothing but harm will come in the long run, from allowing yourself to be exploited, and it is absolutely NOT in ANY way an empowerment of yourself or any other young women."

In response, Cyrus fired off a couple of tweets Thursday, starting with the Irish greeting, "Top of the mornin to ya."

"Before Amanda Bynes .. there was .. ." she said, referring to another troubled former child star, and then posted a screenshot of a series of past O'Connor tweets in which the Irish star referred to her own mental health problems, asking for Twitter followers to recommend a psychiatrist.

Cyrus also tweeted a picture of O'Connor ripping up a photograph of the pope, an infamous on-stage stunt by the singer, who was diagnosed with bipolar disorder.

Cyrus, whose new album is due out in October, provoked a national stir at the MTV Music Video Awards as she performed a raunchy duet with pop singer Robin Thicke.

The "Wrecking Ball" video drew 19.3 million views in its first 24 hours online, setting a record for the Vevo.com website.

[Image via AFP]