An evaluation of reforms to the court system, which were announced in 2012, said almost all trials in sheriff courts in 2016 began within 16 weeks.
Two years earlier that figure was half.
The Scottish Courts and Tribunals Service (SCTS) said this was despite a significant increase in case levels, particularly domestic abuse and sexual violence.
The report said the closure of 17 courts - 10 sheriff and seven Justice of the Peace courts - had been successfully implemented, with savings already realised of Â£2.1m and further annual savings expected of Â£1.3m.
SCTS said while concerns were expressed that court performance would suffer as a result of the transfer of business from smaller centres, there has been "strong and improved performance".
Despite strong local opposition in some cases, the last two courts, Haddington in East Lothian and Dingwall in Ross-shire, closed in February 2015.
It said in all courts, the 16-week waiting period between the first calling availability of a criminal trial was  being achieved.
But it added this had meant some adjustment to the court programme as there was the risk of crown and defence lawyers not having not sufficient time to prepare their cases.
In civil cases, all courts were meeting the 12-week waiting period for civil proofs and hearings, and in most cases they were significantly below that.
SCTS said: "This level of performance continues to be achieved against the background of a significant increase in case levels in both summary and solemn business, particularly in relation to domestic abuse and sexual offences, with a far greater proportion of these cases proceeding to evidence-led trials.
"In April 2014 the percentage of sheriff courts setting criminal trials at the optimum 16 weeks was 50%, at April 2016 this figure is 95%."
Chief executive Eric McQueen added: "For too long it has been easy to describe our criminal courts as products of the Victorian age.
"Our task now is to bring them right into the 21st Century, not by tinkering at the edges, but by radical digital reform to improve the quality of justice for all concerned.
"Through technology we can to allow children and vulnerable witnesses to give their evidence, and have it examined, outwith the trauma and pressures of the court environment and to modernise the way we do business in summary criminal cases through a digital case management system."
Apart from the closure of sheriff and JP courts, the reform package also aimed to concentrate High Court cases in three centres - Edinburgh, Glasgow and Aberdeen.
In the 2016 calendar year these three sites will provide 88% (3,000) of the 3,425 planned sitting days for trials in the High Court.
SCTS has also invested in the development of two new courtrooms in the Glasgow High Court building to be operational by September 2016.
They will add an additional capacity of 500 sitting days per year, reducing the need for the High Court to sit in designated sheriff courts such as Dunfermline, Livingston and Dumbarton which have been used to hear some trials.
Waiting times for trials in Scotland's courts are being reduced, a report has found.