What should we think about ‘acts of conscience’, viz., cases where our personal judgments and public authority come into conflict such that principled resistance to the latter seems necessary? Philosophers mainly debate two issues: the Accommodation Question, i.e., ‘When, if ever, should public authority accommodate claims of conscience?’ and the Justification Question, i.e., ‘When, if ever, are we justified in engaging in acts of conscience – and why?’. By contrast, a third important topic – the Conduct Question, i.e., ‘How should we act, morally speaking, when engaging in acts of conscience?’ – has been mostly neglected. This paper aims to offer concrete guidance for persons wishing to engage in acts of conscience in morally virtuous ways. I argue that such agents are subject to two basic prima facie duties: (i) duties to oneself related to demands of integrity and (ii) duties to others related to demands of civility. I explain both duties in detail, arguing with regard to (i), that in light of what I call ‘the paradox of conscience’, we need to rethink our views about both ‘conscience’ and ‘integrity’; and with regard to (ii), that, building upon Rawls’ ‘duty of civility’, we should embrace at least seven general principles for undertaking acts of conscience in a morally conscientious manner.