The adverb of 'irrepressible': in a way that cannot be held down or kept in. It usually sits before an adjective describing high spirits — irrepressibly cheerful, irrepressibly optimistic, irrepressibly curious — or before a verb about something bursting out: she grinned irrepressibly; the feeling rose irrepressibly in him. It carries the same warmth as the adjective and the same formal, written flavour; you will read it far more often than you hear it.