We find that traditional password advice given to users is somewhat dated. Strong passwords do nothing to protect online users from password stealing attacks such as phishing and keylogging, and yet they place considerable burden on users. Passwords that are too weak of course invite brute-force attacks. However, we find that relatively weak passwords, about 20 bits or so, are sufficient to make brute-force attacks on a single account unrealistic so long as a “three strikes” type rule is in place. Above that minimum it appears that increasing password strength does little to address any real threat. If a larger credential space is needed it appears better to increase the strength of the userID’s rather than the passwords. For large institutions this is just as effective in deterring bulk guessing attacks and is a great deal better for users. For small institutions there appears little reason to require strong passwords for online accounts.