The New Saints' Champions League hopes have been bolstered by long-term injury problems for their opponents. Finnish champions MyPa will be missing star strikers Saku Puhakainen and Niki Helenius in their first-round games set for 12 July and 19 July.
"This has been a problem and it will continue in the early rounds of the season," said MyPa coach Ilkka Makela.
"However, we have signed striker Eero Peltonen, who spent a season playing at Crystal Palace."
MyPa, who dumped Scottish Premier League side Dundee United out of last season's Uefa Cup second round and have also beaten Motherwell, were the second seeds in Friday's draw.
They are currently third in the Finnish league with 15 points from nine games.
The first leg will be in Anjalankoski, the return at Newtown's Latham Park.
The winners advance to the second qualifying round to meet FC Copenhagen over two legs on 25/26 July and 1/2 August.
The victors from that encounter advance to the third qualifying round, that draw to be made on 28 July when another 18 teams enter.
The double-legged third qualifying round will be played on 8/9 and 22/23 August.