Loomis says the Saints have signed cornerback Nick Hixson, guard Paul Fenaroli and tight end Daniel Graham.
Tiller, a 2012 sixth-round pick out of Syracuse, and Davis, an undrafted free agent out of Jacksonville State, were waived because of unspecified injuries.
Bussey was a 2011 seventh-round pick who spent last season on the practice squad.
Graham is in his 11th NFL season after spending last season with Tennessee.
Fenaroli is in his second season. He spent parts of last season on the rosters of Atlanta and Green Bay. Hixson is a rookie free agent out of Hillsdale College.