Used in the '70s, according to three sources.

Trumpet Herald forum, January 15, 2005

2ndchair, 7:23 PM On the album pictures for "You Can't go Home Again" he appears to be playing a Conn Constellation.

I own examples of both and they are very different horns in sound, look and feel.

Chet Baker did suffer from ill health and some extreme dental issues in his later years. The Conn may have felt better on tired chops. Mine sure does!

He still got that fat rich sound and maintained an introverted and poetic style throughout the album. Paul Desmond is also quite amazing and the two musicians are obviously very comfortable working together.

plankowner110, 9:30 PM Chet played a 38B Connstellation. Down Beat magazine did a feature story on Chet along about 1983, and Chet talked about his Conn Connstellation. At the time of the DB interview he was playing a Blessing (you probably can guess why he did not have the Conn anymore) and he said, "I really like Conns but they're so expensive." Chet also stated that he quit playing flugelhorn because it was too much hassle carrying two instrument cases. He said he could achieve the sound he wanted by playing open horn very close to the mic.

I remember that article well because I played a 38B throughout the late 60s, 70s and 80s. I personally knew the regional sales manager for C.G. Conn (pre-UMI) and asked him if Conn would be interested in putting a Connstellation back into the hands of Chet Baker, and he replied that the company probably would not want to use Chet as an endorsee and roll model for student trumpeters. Eventually, Chet dumped the Blessing and picked up a Bach Strad.

The Folk Who Feel Jazz, March 1, 2009

What kind of horns did Chet play?

Chet wasn't loyal to any particular brand or type. He usually blew on whatever he had at the time. Many times he would pawn or lose his horn when he was strung out. He played a Martin "Committee" in the fifties, he even appeared in an ad for Martin. In the 70's he liked the Conn "Constellation". In the 80's he played on a Buescher and a Getzen Capri. At the time of his death he was playing a Selmer "Vincent Bach Stradivarius". He also played a flugelhorn (usually a Selmer) through much of 1964-1968. He found the horn easier to play when he was having problems with his teeth.

Trumpet Herald forum, July 2, 2011

Big Daddy, 1:08 PM According to Ruth Young who dated Chet for 10 years from around 1973 to 1982, the Constellation 38B was his all time favorite trumpet. I've had some long conversations with Ruth, 5 hours once on the phone. She still has Chet's hand written transcript for, "As Though I had Wings" and a couple of his mutes.