They scrapped the original group thing in season 1982-83 (first round was made up of groups - Our group was Dons, Dumbarton, Dundee & Morton)
They then changed it in 1983-84 so that the group stage was brought in at Round 3 - Dons, Dundee, Meadowbank Thistle & St Johnstone.
Scrapped completely in season 1984-85 but kept the 2 legged Semi-finals until the following season.
Maybe we could do what the Germans apparenlty do - Team from lower division is always given home advantage no mater who comes out of the hat first and all games are played to a finish - this should apply to the scottish cup too.