I think strict parents make for secretive kids. If kids feel they don't have a voice, they resort to subterfuge. Rule following is important, but the rules should be negotiable. Having a tight leash and proving that you're in charge can't be more important than communicating with her.

There is obviously something she feels she needs and maybe doesn't feel comfortable telling you. You say she's a good kid, so talk to her. Trust her a little. Let her have a voice in the rules governing her life. All she's being taught right now is to think of ways to outmanuever you.