Comment by squarefoot

Plausible deniability. The system should allow two (or more) passwords, one unlocks only the important stuff and one unlocks much less dangerous stuff while destroying any evidence of the first, including the multiple passwords protection layer. To add some credibility, the less dangerous data should contain something one could get in trouble for but not enough to have his life destroyed. As an example, if after being forced to reveal a password my phone showed photos of myself having sex with a hooker, I don't think many prosecutors would believe I put them there to protect other more sensitive stuff that would ruin my entire life and not just my relationship. And if they did, I just served them with real proof of why I encrypted my phone which should be enough to counter their unfounded accusations.