Just Like That was written by Björn and Benny in May 1982, and recording sessions began that same month. At least three versions were recorded: the first attempt at recording the song has become known as the 'original', 'slow' or 'dream' version (the version used in my video here). The second version of the song is known as the 'Nanana' or 'Lalala' version. The last known version of the song has become known as the 'saxophone' version.
After recording of the 'saxophone' version in June 1982, Just Like That was left unsatisfactory by Benny and Björn. They stated some time afterwards that the song simply sounded 'wrong': the verses and the choruses did not go together well, and that is why it was scrapped.
Ah well, we can always hope they'll change their minds. :)