The Cowboys and all other teams can start signing unrestricted free agents today without compromising possible compensatory picks coming their way in 2016.
For years, June 1 was an important date for NFL teams, because after June 1, unrestricted free agents signed by other teams didn't count against a team's compensatory draft-pick formula. Starting in 2015, that date has been moveed from June 1 to May 12, according to the league office.
The move was made to incentivize teams to sign veteran free agents shortly after the NFL draft instead of waiting until shortly before camp to sign veterans, as they had done in the past.