Two more veterans landed with NHL teams on Tuesday as centre Jeff Halpern signed a one-year, $600,000 (U.S.) contract with the Montreal Canadiens and former Leafs centre Kyle Wellwood agreed to a training camp tryout with the Phoenix Coyotes.
While there are still quite a few free agents left to be signed, Burke said he would not be adding any more bodies to his lineup.
"We're going with this [roster]unless something miraculous happens," he said. "This is the group. We're going to start with this."
Burke added that he expected the Leafs will be improved because they would have recently acquired players such as Phil Kessel, Jean-Sébastien Giguère, Dion Phaneuf and Fredrik Sjostrom for a full season.
Among the unrestricted free agents still searching for contracts are Brendan Morrison, Darcy Tucker, Jose Theodore, Bill Guerin, Marek Svatos, Ray Emery, Owen Nolan, Ruslan Fedotenko, Marc-Andre Bergeron, Nigel Dawes and Patrick O'Sullivan.