Europa Conference League is the European Football Association's UEFA's newly started club team tournament, the third most prestigious after the Champions League and Europa League.
On Thursday, Elfsborg, Häcken and Hammarby will enter the ECL's second qualifying round of four.
The three Swedish teams finished second, third and eighth in the Allsvenskan last year, behind the champion team Malmö FF who qualify for the Champions League.
"Bajen" got a European qualifying place thanks to the Swedish Cup final victory against Häcken at the end of May.
Both Elfsborg and Hammarby impressed when the blue and yellow clubs made their entrance in the new European Cup.
Three reds out of ten
The Borås team was superior to Moldavian Milsami and won 4-0 after goals from the Finn Leo Väisänen (already after just over a minute of play), the Danes Jeppe Okkels and Frederik Holst and Per Frick.
Elfsborg thus stands with one leg in the third qualifying round before the meeting in Orhei next week.
Three players who miss the return, however, are Milsami's Vadim Dijinari, Vitus Amougui and Vadim Bolohan.
All three were sent off, within ten minutes of the second half.
Dijinari after a straight red card and Amougui and Bolohan after two warnings each that rendered in red for both.