The invention encompasses constrained bicyclic and tricyclic CGRP-receptor antagonists, methods for identifying them, pharmaceutical compositions comprising them, and methods for their use in therapy for treatment of migraine and other headaches, neurogenic vasodilation, neurogenic inflammation, thermal injury, circulatory shock, flushing associated with menopause, airway inflammatory diseases, such as asthma and chronic obstructive pulmonary disease (COPD), and other conditions the treatment of which can be effected by the antagonism of CGRP-receptors.