In recent work on open, privacy-preserving, accountable surveillance, we have proposed the use of cryptographic protocols that enable law-enforcement and intelligence agencies to obtain actionable information about targeted users of mass-communication systems without intruding on the privacy of untargeted users. Our suggestion that appropriate technology, combined with sound policy and the rule of law, can afford typical users significantly more privacy than they have now without hindering lawful and effective actions by law-enforcement and intelligence agencies has met with considerable skepticism. In this paper, we summarize the principal objections to our approach and address them.