Coding a rectangular box with rounded corners (with CSS)

How do I code this in CSS:



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I usually tackle this by slicing it into three parts: the top (1), the liquid middle (2), and the bottom (3), as shown on the image below:



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However, I found that the rectangular boxes (with rounded corners) on this website load such a way that each rounded corner loads at different times. This should mean that a different image is used for each rounded corner, and is a totally different method of slicing and coding.

My questions are:
1. How do you code using the second method described above?
2. Which method is better?

Thanks!