Ah, that might indeed be a solution, I'll look into that option!
It's a swedish module called Fraktjakt - https://addons.prestashop.com/en/shipping-carriers/17108-fraktjakt-swedish-shipping-integration.html
In the stores I'm currently using PS 1.6, payment modules can only be restricted by currency or country,
if I would like to restrict by carrier there is third party modules for that, but nothing pre-installed.