In his native Finland Koivistoinen has worked with nearly every Finnish jazz musician and a great number of ensembles. The most important employer in 1975 – 90 and 1996 – 98 was the UMO Jazz Orchestra, where Koivistoinen worked as a saxophonist, conductor and artistic director with several legendary jazz musicians. The list of his foreign co-players has names like this:
Dizzy Gillespie, Charlie Mariano, John Scofield, Ron McClure, Jack DeJohnette, Idrees Sulieman, Randy Brecker, Tom Harrell, JimMcNeely, Conrad Herwig, Slide Hampton, James Moody, Clifford Jordan, Dexter Gordon, Art Farmer, Gil Evans, Thad Jones, Mel Lewis, Billy Hart, George Russell, Mike Gibbs, Ted Curson, Helen Merrill, Bob Brookmeyer, Clark Terry, Dave Kikoski, McCoy Tyner, Tim Hagans, Joe Henderson, Oliver Nelson, Mercer Ellington, Ray Anderson, Niels Henning Örsted Pedersen, Jesper Lundgaard, Leroy Lowe, Anders Bergcrantz, John Tchikai, Allan Botchinsky, Alex Riel, Palle Mikkelborg, Mario Bauza, Dave Liebman, George Wadenius, Philip Catherine, Sabu Martinez, Bertil Lövgren, Bernt Rosengren, Lasse Lindgren, Jeff Hirshfield, Kenny Drew, Claudio Roditi, Azymuth, Paquito Rivera, Abe Laboriel, Justo Almario, Kevin Hayes, Benny Carter, Red Mitchell, Don Menza, Bengt Hallberg, Etta Cameron, Eddie “Lockjaw” Davis, George Fame, Benny Golson, Herb Geller, Jerry Dodgion, Bill Holman, Muhal Richard Abrams, Louis Bellson, Johnny Griffin, Louis Stewart, Mario Grillo, Herb Pomeroy, Dino Saluzzi, Mike Nock, Mike Westbrook, Larry Coryell, Zoot Sims, Graham Collier, Jeff Williams, Bob Berg, Albert Mangelsdorf, Senegalese Drums, Galaxy, Eduardo Durao, Gloria Bosman, Concord Nkabinde, Barry Van Zyl, Lulu Gontzana, Kenny Washington, Alan Jean-Marie, Horace Parlan, Alvin Queen, Bennie Wallace