My current job hired me at a 40% raise. This was after telling them exactly what I made. And I did exactly what you said: I told them I knew I was underpaid.

Now, I'm pretty sure I could have gotten another 10-20% if I had not given them this information. But really, I'm getting paid what the job's worth, so I'm not complaining. If I thought the job was worth more, I'd have held out for the last bit. They did mention my existing lower salary as a reason they couldn't offer more, too.

I understand both sides of that. They have to be sure I wasn't being paid low because I can't perform, and I want to get paid what I'm actually worth. When you're as badly underpaid as I was, it's rough. I should never have let myself get into that position.