How can I stick to the rules with my teenager?

Q: One of the difficulties I have with my 14-year-old daughter is sticking to what I say. For example, my daughter did something that I was clear about her not being allowed to do. So I told her she was grounded for the week. After two days of being grounded she said she was sorry and learned her lesson (there just happened to be a party she wanted to go to the next day). She then went on to explain why I should allow her to get off being grounded – and, to tell the truth, it was really logical. So after an internal struggle I said okay.