In episodic memory research, there is a debate concerning whether decision-making in item recognition and source memory is better explained by models that assume all-or-none retrieval processes or continuous underlying strengths. One aspect in which these classes of models tend to differ is their predictions regarding the ability to retrieve contextual details (or "source" details) of an experienced event, given that the event itself is not recognized. All-or-none or high-threshold models predict that when items are unrecognized, source retrieval is not possible and only guess responses can be elicited. In contrast, models assuming continuous strengths predict that it is possible to retrieve the source of unrecognized items, albeit with low accuracy. Empirically, there have been numerous studies reporting either chance accuracy or above-chance accuracy for source memory in the absence of recognition. Crucially, studies presenting recognition and source judgements for the same item in immediate succession ("simultaneous design") have revealed chance-level accuracy, while studies presenting a block of recognition judgements followed by a block of source judgements ("blocked design") have revealed slightly above-chance accuracy. Across three sets of experiments involving multiple design manipulations, the present investigation demonstrated: (a) that source memory for unrecognized items is indeed higher in blocked designs; (b) that evidence for the effect in blocked designs is likely artifactual due to item memory changing between blocks; and (c) that the effect does exist in simultaneous designs, but is highly subtle and is more easily detected when uncertainty in the participant-level data is low or is accounted for in a hierarchical Bayesian model. It is suggested that findings of a null effect in the prior literature may be attributable to design elements that hinder source memory as a whole, and to high degrees of uncertainty in the participant-level source data when conditioned on unrecognized items.