St Johnstone have signed striker Graham Cummins, but former Scotland forward James McFadden and defender Gary Miller have not been offered new deals.
Cummins, 27, who has signed a one-year deal, scored seven times for Exeter City last season.
Manager Tommy Wright told the St Johnstone website: "I know quite a bit about him and he trained with us towards the end of the season.
"He scored a lot of goals for Cork City before a move to Preston North End."
The Reading-born player has had spells with Cobh Ramblers, Waterford United, Cork City, Preston North End and Rochdale.
On the decision to let Miller and McFadden go, Wright said his club were in need of fresh faces, with Joe Shaughnessy already signed from Aberdeen and Brad McKay arriving from Hearts.
"Gary has been an important member of the squad for me and has played his part in the success we have had, but with Joe Shaughnessy and Brad McKay coming in, I feel it's time to freshen things up at the back," he said.
"Faddy came in at an important time of the campaign and his experience has been a huge help to us both on and off the park."
The 32-year-old McFadden, capped 48 times for his country, had joined Saints in October after being released by Motherwell last summer.
He made 20 appearances for the Perth club, half as a substitute.
The 28-year-old Miller, who made 26 appearances this season, joined St Johnstone after leaving Ross County in 2012.