The promises of smart cities continue to overwhelm many people eager to live in them. Simultaneously, many people are still concerned about the increasing privacy risks associated with the core of the promises. The core of smart cities' promises lies in generating and using data to enable urban technologies that provide, to some degree, value-added services and opportunities for both cities and their citizens. The promises of smart cities highlight three interdependent dimensions, namely the information type, purpose, and value that provide the basis of studying and addressing privacy concerns to enable successful smart cities. This paper presents a 3D privacy framework based on three interdependent dimensions that build on existing citizens' privacy models  and framework  to hypothesize when citizens are likely to accept smart city technologies with privacy concerns, when citizens are more likely to accept trading their privacy for the provided valued services under defined regulations, and when citizens are likely to protest and disregard smart cities technologies altogether. The 3D privacy framework highlights new ways of evaluating how technologies impact citizens' privacy and encourages adopting new ways to lessen citizens' privacy concerns by implementing technology-specific agile regulation based on the metrics of security. Some specific examples of smart city technologies are discussed to illustrate the practicality and usefulness of the proposed 3D privacy framework in the smart cities' space.