Relief Pitchers have a lot of wiggle room as far as the starting season as many relievers will have seasons below $3 mil.
Take the first $3 mil+ season, or pick an earlier season & start from there.
Let's take Billy Wagner for example. First $3 mil+ season is 1999.
You can start his career in the League there, or choose to start it in 1996, 1997, or 1998 as they are all under $3 mil.
Regardless come 2000, you've got a decision to make. Do you carry his crappy 2000 season on your roster or cut him? If you cut him he is a Cut Free Agent and can be drafted by anyone for that 2000 season. Most likely someone would scoop him up for his future value and eat the 2000 season. BUT if everyone passed on him, come the NEXT season, he would be an eligible Free Agent for the 2001 season.
Wagner, Billy
1996 Houston Astros L 52 2 2 9 2.44 1.12 .165 11.67 5.23 $1,569,665 A+/D-
1997 Houston Astros L 67 7 8 23 2.85 1.19 .204 14.38 4.07 $1,985,758 D/D
1998 Houston Astros L 60 4 3 30 2.70 1.18 .211 14.55 3.75 $1,719,218 D-/D-
1999 Houston Astros L 75 4 1 39 1.57 0.78 .135 14.95 2.77 $4,314,571 A+/D-
2000 Houston Astros L 28 2 4 6 6.18 1.66 .255 9.11 5.86 $294,805 A+/D
2001 Houston Astros L 63 2 5 39 2.73 1.02 .198 11.35 2.87 $2,063,177 D/D
2002 Houston Astros L 75 4 2 35 2.52 0.97 .196 10.56 2.64 $2,596,953 A+/C-
2003 Houston Astros L 86 1 4 44 1.78 0.87 .169 10.99 2.41 $3,708,768 A+/B-