Calls, but no message left

My answering machine picked up before I could answer the call and so the system  disconnected.   Called the number back and it was a Telemarketing Firm.  Computer answered and I pressed 1 for them not to call again.   But the problem is I 'm on both Federal and State do not call lists.

i got a call from this number. it rang once before i picked it up. there was no one on the line. no message.

I picked up after it rang a couple of times.  NO ONE there.
I called # back and pressed 1 to get on their Do Not Call list.

This is at LEAST the 3rd call ... a recording that says something to the effect that this is your last chance to stop over-paying interest on your credit card account ... We've been getting the same calls on both of our land lines - both are on state and federal "no call" lists. We have a terminally ill person in our home. We hate these calls.