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Entertainment Weekly reports that Morse's role as police lieutenant Terry Colson has been promoted from recurring to full-time. The actor originally joined the show midway through the first season.
Morse previously received an Emmy nomination for his recurring role as Detective Tritter on House and also played George Washington in 2008 HBO mini-series John Adams.
Ennega will now appear on a regular basis as Sofia Bernette, the daughter of English teacher Creighton (John Goodman). The 15-year-old actress previously starred alongside Meg Ryan in 2008 film The Women.
Treme is expected to return to HBO in early 2011.
