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First round of iPhone 4 preorders sold out now shows an expected ship date of July 2, instead of June 24. AT&T also says it can no longer take orders for June 24.

iPhone 4 preorder says iPhone 4 preorders as of Tuesday night will arrive on July 2 at the earliest. Screenshot by Erica Ogg/CNET

Despite a disastrous preorder process Tuesday morning, enough people were able to place iPhone 4 orders that much of Apple's initial U.S. supply has already been accounted for.

As of Tuesday evening, now shows that iPhone 4 preorders will be shipped by July 2. The device actually goes on sale for the first time June 24, and that was the expected shipping date for customers who placed a preorder earlier in the day. AT&T said it also can no longer take preorders for June 24.

AT&T is now saying, "Because of the incredible interest in iPhone 4, today was the busiest online sales day in AT&T history. As of Tuesday afternoon, customers who preorder iPhone 4 moving forward will receive their device on June 25 or later, depending on when the order is placed.

Despite the sold-out preorder supply, it won't be entirely impossible to get an iPhone 4 next week. Both Apple and AT&T stores keep a supply for walk-in customers starting on June 24. Other options that day include Best Buy, Radio Shack, and Wal-Mart. Those three retailers will also sell the iPhone 4 in stores starting June 24.