According to Dansk Biografisk Lexikon, King Frederik IV recognized Duke Carl Christian's son Frederik Christian as of equal, princely birth and able to succeed to the Dukedom of Plön, which he was in line to inherit from his uncle, by making his mother a Princess of Denmark. In return Frederik Christian gave up his inheritance in Schleswig, i.e. parts of the islands of Als and Ærø, to the King.
He succeeded as Duke of Plön, but as he had only daughters (who perhaps might not have been ebenbürtige, as their mother was a mere Countess Reventlow, although she was the niece of King Frederik IV's morganatic wife), he agreed in the so-called Plönisches Successionstraktat to leave his Duchy to the King of Denmark when he died in 1761. In return King Frederik V paid all of his large debts.
Twelve years later the remaining part of Holstein-Gottorp did of course also revert to the King of Denmark through that brilliant Treaty of Tsarskoe Selo. Only that odd Bishopric of Lübeck remained...