You see, the ADSL modem is associated with the normal phone line. And if you want to move your ADSL, you'll first have to move the normal phone, and then afterwards you can order the move of the ADSL -- at a price of about 100 euros, and you'll be offline for about a week, possible 10 days.
The helpdesk-guy had a helpful suggestion: take a new phone line at your new address, then order ADSL for that line (at no cost), and cancel your current ADSL subscription (again, at no cost). There could be an actual overlap in ADSL service, too!
Given the fact that I am much more attached to the ADSL connectivity than our actual phone number (most people know how to contact us via other routes anyway), this was the way to go. There are a few other benefits: we could chose not to add our number to the registry, which means we'll get less calls from direct marketing people.
It took the lady from the phone company a few minutes to understand what it was we wanted, but, to her credit, she accepted the fact that we had thought about it and didn't try to convince us otherwise.
A few hours after getting the key, we'll have our new phone number! Tomorrow I'll call the provider to order ADSL in our new house!