Brainwallets shouldn't be casually recommended without appropriate warnings, but they certainly can be secure.
Passphrases aren't limited by length, and your brainwallet can be derived from your memory and publicly available information, so you can construct very strong memorable passphrases, e.x. the 3rd sentence of the 8th chapter of your favorite book concatenated with a moderately strong but memorable password.
Key stretching with PBKDF or scrypt helps a lot as well. Do you care if it takes 1 minute to compute your keys from the passphrase? Probably not, and it will make cracking much more difficult.
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Brainwallets shouldn't be casually recommended without appropriate warnings, but they certainly can be secure.
Passphrases aren't limited by length, and your brainwallet can be derived from your memory and publicly available information, so you can construct very strong memorable passphrases, e.x. the 3rd sentence of the 8th chapter of your favorite book concatenated with a moderately strong but memorable password.
Key stretching with PBKDF or scrypt helps a lot as well. Do you care if it takes 1 minute to compute your keys from the passphrase? Probably not, and it will make cracking much more difficult.
Even extending to a 1-second computation would make it completely infeasible to crack. 1 minute would be way overkill.
Well, whether it's overkill depends on how weak your passphrase is.