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In Islamic Law, tazir (or ta'zir, Arabic تعزير) refers to punishment, usually corporal, that can be administered at the discretion of the judge, called a Qadi, Kadi,  as opposed to the hudud.  The Oxford Islamic Studies defines the six crimes for which punishments are fixed as theft (amputation of the hand), illicit sexual relations (death by stoning or one hundred lashes), making unproven accusations of illicit sex (eighty lashes), drinking intoxicants like alcohol (eighty lashes), apostasy (death or banishment), and highway robbery (death). Strict requirements for evidence (including eyewitnesses) have severely limited the application of hudud penalties.
The punishments for the Hadd offenses are fixed by the Qur'an or Hadith, however ta'zir refers to punishments applied to the other offenses for which no punishment is specified in the Qur'an. These are often the equivalent of misdemeanor offenses. They could also be applied to hadd offenses in situations where the standards of proof required for hudud punishments could not be met due to their strict nature. The general rule dictates that no Ta'zir punishment can exceed that of a hadd penalty.
Ta'zir developed in the early Islamic empire of the Umayyads (A.D. 661-750). The objectives of the punishment was to discourage repetition of the crime. This was accomplished by varying the punishment to fit the circumstances of the convicted party, particularly if reparations were made or repentance shown to the offended party. Punishments ranged from admonitions to death, though death is only used in extreme cases.
The burden of proof is less strict in a Ta'zir case, the testimony of two witnesses or a confession is enough. Confessions are not able to be retracted later.