[susan53]

How about...

I didn't get good grades while I was taking the course (so in the end I gave up)

I didn't see the car coming while I was crossing the road (but luckily it stopped in time)

When I was learning to swim, I didn't enjoy it at all (but now I love it.)

I didn't answer the phone while John was having a shower (because I knew it would be his mother and I can't stand her.)

We didn't go out while it was snowing (but after it stopped we went for a walk.)

While I was staying at the hotel, I didn't need to cook (which for me was the best part of the holiday).
etc etc etc

The parts in italics are examples which show that - yes you can. The parts in brackets are just there to add context.