Every couple reconciles differently after a tiff. Paul Simon and Edie Brickell have done it with a new song.

Within days of appearing in court together on disorderly conduct charges, the celebrity couple have recorded a love duet, titled Like To Get To Know You, and released it to Brickell's personal website.

Simon and Brickell were arrested at their home in New Canaan, Conn., last Saturday night by officers investigating a physical altercation.

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Simon, 72, and Brickell, 47, held hands during their appearance in Norwalk Superior Court on Monday, with Simon telling the presiding judge, "Both of us are fine together. We had an argument. It's atypical."

In court, Brickell said, "He's no threat to me at all."

The judge ordered the couple to return to court on May 16.

That same day, Brickell expanded on the incident to Rolling Stone (through her attorney) by saying, "I got my feelings hurt and I picked a fight with my husband. The police called it disorderly. Thank God it's orderly now."

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But the real healing between Simon and Brickell, who have been married since 1992 and have three children together, was evinced in the new song, which Brickell posted to her website on Wednesday.

Both Simon and Brickell's distinct vocal talents are clear in the country-tinged song, which makes reference to a couple that has "lost touch," but also includes the repeated refrain, "I wouldn't trade places with anyone."

The couple's new song may not exactly hold the emotional heft of Simon's 1970 hit Bridge Over Troubled Water with partner Art Garfunkel - but it's a step in the right direction.