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Apple says it is making progress toward creating enough Apple Watches to go around.

While Apple is giving no sales numbers, the company is said to have sold almost a million Watches on the first day of preorders back on April 10. However, many would-be buyers either weren’t able to get the watch they wanted, or they bought one and then saw that the delivery date was far in the future.

“Right now the demand is greater than the supply,” Cook told analysts during an earnings call today. “It is a new product, and you wind up taking some time to fully ramp up,” he said.

Apple believes it can do this soon. “Sometime in late June we hope to be in a position where we can begin to sell the Apple Watch in other countries. That’s our current plan,” he said.

Apple hopes to sell 20 million of the devices during 2015, which would make it the biggest product launch in Apple history.

“We’ve been making progress over the last week,” Cook said, adding that some Watch delivery dates have been moved up.

“We’ve already sent notes out today moving customer deliveries in, versus what we told them originally,” the CEO said.

Apple also says it’s learning important lessons about consumer preferences among the many models and styles of Watches available. Cook said he feels that Apple correctly anticipated many Watch and band styles people wanted, but in other cases the company needs to make adjustments in its product offering.

Cook didn’t provide specifics on which watches and bands were not connecting well with consumers. (Hint: Puke green Sport Watch.)

Cook’s remarks came after Apple announced its second-quarter earnings today. The company reported strong results, helped by continued strong iPhone sales in the U.S. and China.

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