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How do I put my document in strict (standards-compliant) mode?

In short, you add a DOCTYPE. An XHTML or HTML Strict DOCTYPE will accomplish it just fine in all browsers. If you want to see the details for each browser, see below:

IE 6 (Windows): MSDN on !DOCTYPE Switching

Mozilla and Safari: Mozilla's DOCTYPE sniffing

Opera: DOCTYPE Switching in Opera

IE 5 (Mac): Eric Meyer's Summary

Henri Sivonen's DOCTYPE switching analysis