Payment above or below the value of the actual damage inflicted is considered a fine rather than a payment of reparations: Bava Kama 15b; Sanhedrin 3a-b
Procedure
Fines may not be collected outside Israel: Bava Kama 15b
Where a the victim collected money by force outside Israel, the Court doesn't retrieve it from him: Bava Kama 15b
Court setting up a time, enforced with Ex-Communication for the parties to travel to Israel for Collection: Bava Kama 15b
Requiring Expert Judges to levy fines: Bava Kama 14b
Whether one pays a fine if he admits the crime, himself: Bava Kama 14b-15a, 15b; Bava Metzia 3b, 34a; Makkot 2b
Where One admits the crime, but then Witnesses come who would have incriminated him without his admission: Bava Kama 14b-15a
Fines levied to prevent a Sinner from being Rewarded
One who rapes a convert while she is a Minor, so she can return to Nochri status: Ketuvot 11a