Etymology of tiramisu

This is really a question for an expert in Italian. I've seen a couple of different explanations for the name of the popular Italian dessert, tiramisu (accent grave over the "u"). Clearly it means "pick me up" but in what sense? One far-fetched theory has it being invented near a brothel and referring to the women you could "pick up" there.

The more common explanation is that the stimulating qualities of the chocolate and coffee give you a real "pick me up." I must say a dish of rich, creamy tiramisu is more likely to send me into a lethargic slumber, despite its caffeine content.
I've always imagined the phrase simply referred to the dessert's irresistible appeal, and that "tiramisu" meant something very like the "eat me" label on the cakes that Alice in Wonderland nibbles on: "pull me up into your mouth."
Is there anyone who knows for sure what Italians themselves think of when they use this phrase in relation to the dessert?

Paul Brians