In Estonia the last execution took place on the 11th of September 1991 when Rein Oruste was shot with a bullet to the back of the head for the crime of murder. The death penalty was completely abolished in Estonia on the 18th of March 1998 when Protocol No. 6 to the ECHR was signed.
From 1 February 1920 to the incorporation into the Soviet Union in 1940, inmates condemned by civilian courts were given the right to choose how they died: either suicide by drinking poison or hanged in the following terms (as stated in the Criminal Procedure Code which entered in force on 1 February 1935): "One hour before the scheduled time of the execution, the condemned shall be taken to a death cell, where the state prosecutor will read the death sentence and ask the prisoner whether he is willing to commit suicide. If the answer is in the affirmative, the prosecutor will hand the condemned a glass of poison—the kind of poison to be determined by the National Health Board. If the doomed man fails to take the poison within five minutes he will be hanged'" Military executions were carried out by an eight men firing squad.
http://nla.gov.au/nla.news-article2311219