Freshwater shortage in Southern California - What do you think about the idea of using icebergs as a new source of fresh water?

From “How Stuff Works”: Fresh water is scarce in many parts of the world. Places like Southern California, Saudi Arabia, and many countries on the African continent can use all the fresh water they can get. Something like 70 percent of the Earth’s fresh water is locked up in the polar ice caps, and the ice caps calve icebergs naturally all the time. It therefore makes sense to think about towing huge icebergs to the places in the world that need fresh water the most. The first problem is melting. If you’ve ever run tap water over an ice cube, you know that even cold running water can melt an ice cube very quickly. It’s the same effect that causes wind chill, but with running water, the effect is even greater. The second problem is the draft of an iceberg. The expression “tip of the iceberg” comes from the fact that almost all of an iceberg is submerged under water. A big iceberg is hundreds of feet deep.

To solve both of these problems, it might be easier to mine the icebergs in the Arctic and fill up supertankers with ice shavings. Modern supertankers can hold something like 100 million gallons of liquid. That’s a drop in the bucket compared to the 20 billion gallons in an iceberg, but it would be a lot quicker and easier to move the water around in a supertanker.

http://science.howstuffworks.com/icebergs-as-water.htm/printable

What are your thoughts? Is it a totally crazy idea? A last resort? Is desalination a more promising approach?