Generally, if an accused has been already been convicted of an offence, or acquitted of an offence, he cannot again be convicted of the same offence arising from exactly the same circumstances. The judge has a discretion to stay a second set of proceedings arising out of the same or substantially the same circumstances unless the prosecution establishes that because of special circumstances there should not be a stay: Connelly  AC 1254, Beedie  2 Cr App R 167, The Queen v Carroll (2002) 213 CLR 635.
However, exceptions have been created to this rule by statute. On application by the DPP, the Court of Criminal Appeal may order that a person who has been acquitted be retried for an offence carrying a maximum penalty of life, if there is fresh and compelling evidence of the guilt of the accused, and if it is in the interests of justice for the order to be made: s. 100 Crimes (Appeal and Review) Act. Evidence is ‘compelling’ if it is reliable, substantial, and highly probative in the case against the accused: s. 102 Crimes (Appeal and Review) Act.
On application by the DPP, the Court of Criminal Appeal may order that a person who has been acquitted be retried for an offence carrying 15 years or more gaol as a maximum penalty, if someone has been convicted of an administration of justice offence relating to the earlier trial (for example, perjury), and if it is more likely than not that, but for the commission of the administration of justice offence, the accused would have been convicted: s. 101 Crimes (Appeal and Review) Act.
Autrefois convict does not apply where there are convictions for two different offences constituted by the same act: Pearce v The Queen (1998) 194 CLR 610. However, in a situation where an accused is charged with an offence, and is acquitted, and is later charged with a second offence arising out of the same circumstances, autrefois acquit may apply if either all the elements of the first offence are contained within the second offence, or vice versa: Island Maritime v Filipowski (2006) 228 ALR 1 esp at paras  (per Gummow and Hayne JJ) and  (per Kirby J).
By analogy with autrefois acquit, where a person has been acquitted of an offence after giving evidence, a charge that the accused committed perjury by asserting his innocence should be stayed: The Queen v Carroll (2002) 213 CLR 635.