The Giants have signed fifth-round draft picks linebacker Ryan Connelly and wide receiver Darius Slayton and re-signed defensive tackle John Jenkins.
Still unsigned are No. 1 draft picks quarterback Daniel Jones, defensive tackle Dexter Lawrence and cornerback DeAndre Baker, as well as third-rounder outside linebacker Oshane Ximines and cornerback Corey Ballentine, who is still recovering after being shot in the glutes.
Other members of the draft class who have signed include fourth-round cornerback Julian Love and seventh-rounders tackle George Asafo-Adjei and defensive lineman Chris Slayton.
Jenkins, a journeyman who has been with the Saints, Seahawks and Bears, played in seven games last season for Big Blue and was inactive for nine.