The are also direct trains to Prague, which made for a nice side trip when I needed to go to Leipzig.

They're longer, about 3h I think.

Thanks for the recommendation !

Sadly I can only recommend against that. Because you can't book them together you need to plan in a lengthy stop in case of delays. I made that mistake twice and both times I was badly burned.

I took the train from Copenhagen to Leipzig.

It's a bit too long, but I met my Swedish friends on the platform at Hovedbanegård, and they'd already started the party with "cheap" alcohol from Netto.