Governments around the world are seeking to slow the spread of Covid-19 by implementing measures that encourage, or mandate, changes in people's behaviour. These changes include the wearing of face masks, social distancing, and testing and self-isolating when unwell. The success of these measures depends on the commitment of individuals to change their behaviour accordingly. Understanding and predicting the motivation of individuals to change their behaviour is therefore critical in assessing the likely effectiveness of these measures in slowing the spread of the virus. In this paper we draw on a novel framework, the I3 Compliance Response Framework, to understand and predict the motivation of residents in Auckland, New Zealand, to comply with measures to prevent the spread of Covid-19. The Framework is based on two concepts. The first uses the involvement construct to predict the motivation of individuals to comply. The second separates the influence of the policy measure from the influence of the policy outcome on the motivation of individuals to comply. In short, the Framework differentiates between the strength of individuals' motivation and their beliefs about the advantages and disadvantages of policy outcomes and policy measures. We found this differentiation was useful in predicting an individual's possible behavioural responses to a measure and discuss how it could assist government agencies to develop strategies to enhance compliance.