The paper explores a common core of meaning that various aspectual adverbials in Hungarian (including megint, ismét ‘again’, még ‘still’) share. It is proposed that there is a general definition for various aspectual elements related to times and events. We suggest that some components of those elements, including the scalar argument and the focus set, can vary – and this results in the different specific meanings. We assume that meaning is compositional and also address the complex form mégis ‘(concessive) still’ and other elements that appear to be synonymous with mégis.