May I compliment you?

I realized the other day that I have serious problems giving and receiving compliments. I think this may mean I don't give (or get) enough of them because one usually improves at something with practice. In my experience compliments just tend to put an end to the conversation. Consider the following scenario. Two people are talking. One tells the other how nice she is. The one receiving the compliment says thank you. And then what? Where do you go from there? Exactly. The flow of the conversation is gone and you have to come up with a completely new topic in order to finish the conversation.
Now I, being the amazing person that I am, developed a strategy to prevent this after compliment awkwardness. Sarcasm. It is probably the worst strategy I ever could have come up with. Whatever the compliment was or who gave it, sarcasm can easily reverse the meaning. And that is not at all what I want to do. It's just all I know how to do. So I tell people they're beautiful and follow it up with "compared to what they used to look like," or someone tells me I have a wonderful smile and I have to say "too bad no one ever sees it" or something like that. So if someone tries to give me a compliment it is the easiest thing for me to put myself down. Clearly something isn't right. Compliments are meant to make you fee better not worse, and they can stand alone. Who cares if they kill the conversation? I'm sure I can figure out something else to talk about and I'll keep the joy of giving or receiving a compliment without having to kill the mood. So with that said, may I compliment you?