Someone please chime in here with some training threads, and a little bit about positive reinforcement.
You're right, no popping or spanking. You really don't need it, if you can get the positive reinforcement part down. And it could even make things harder in the long run. Especially with a young pup.
Have you tried some outside help? A trainer, or even a puppy class?
The trick isn't getting them to "realize that's wrong," so much as getting them to realize what's Right.
Are you using a clicker? The treat won't work if theres a time lag between the wanted behavior and the reward...and 2 seconds to a puppy is a time lag.