The decisions Saturday left players with a 5-2 record this year. There are 18 players scheduled for hearings in the next two weeks.
Giles got a raise from $555,100 to $4.6 million -- $400,000 more than Houston's offer. This was the first time he was eligible for arbitration.
Giles went 34-for-38 on save chances last season and was 1-3 with a 2.30 ERA. He struggled as the Astros won their first championship, posting an 11.74 ERA in the postseason and 27.00 ERA in a pair of World Series appearances, when he allowed five runs in 1 2/3 innings.
Hechavarria, who made $4.35 million last year, was awarded $5.9 million, instead of the $5.35 million offered by the Rays. He hit a combined .261 with eight homers and 30 RBIs last season, when he was traded from Miami to Tampa Bay in late June.
Osuna, also eligible for arbitration for the first time, will make $5.3 million after asking for $5.8 million. He made $552,400 last year when he was 3-4 with a 3.38 ERA and 39 saves while also leading the majors with 10 blown saves.