Cannot Delete a Conversation Without Deleting the Contact

With previous ios on the iPhone, I could delete an entire conversation within a text message on the iPhone (4S).

It appears that with ios7, I cannot delete just the conversation. If I hit Delete, it deletes the recipient's contact info, as well.

Is this correct, or am I missing something?

Thank you.

Are you sure? When I swipe either right or left, nothing happens. That only works to delete the entire message.

That got me just what I had wanted to do.

Thank you!