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The 26-year-old Surkamp, a sixth-round pick by the Giants in the 2008 amateur draft, went 0-1 with a 23.63 ERA in one spot start for San Francisco last season that lasted only 2 2-3 innings on July 23 against his hometown Reds. He was 7-1 with a 2.80 ERA between Class A San Jose and Triple-A Fresno.
He sat out the 2012 season because of an elbow injury.
Morel appeared in 12 games for Chicago last season and hit .200. He has a .229 average in 194 games.
The moves announced Monday put Chicago's 40-man roster at 40.