Epistemic modals are used to convey judgments about the probability of an event (cf. Palmer 1990: 50f). In Present-Day New Zealand English, epistemic utterances that concern past events usually contain a ‘perfective’ have that follows the modal. However, especially in the speech of NZers born between the late 19th and mid-20th century, we also find utterances where no have is present, even though a past event is discussed. This paper investigates the influence of linguistic factors on the use of perfective have in noncounterfactual judgments involving epistemic modals. I argue that the additional have may serve either to mark past time, or the episodic nature of the assessed event, and I propose that its distribution is determined by considerations of economy.