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The ability to distinguish between different explanations of human memory abilities continues to be the subject of many ongoing theoretical debates. These debates attempt to account for a growing corpus of empirical phenomena in item-memory judgments, which include the list strength effect, the strength-based mirror effect, and output interference. One of the main theoretical contenders is the Retrieving Effectively from Memory (REM) model. We show that REM, in its current form, has difficulties in accounting for source-memory judgments – a situation that calls for its revision. We propose an extended REM model that assumes a local-matching process for source judgments alongside source differentiation. We report a first evaluation of this model’s predictions using three experiments in which we manipulated the relative source-memory strength of different lists of items. Analogous to item-memory judgments, we observed a null list strength effect and a strength-based mirror effect in the case of source memory. In a second evaluation, which relied on a novel experiment alongside two previously published datasets, we evaluated the model’s predictions regarding the manifestation of output interference in item and lack of it in source memory judgments. Our results showed output interference severely affecting the accuracy of item-memory judgments but having a null or negligible impact when it comes to source-memory judgments. Altogether, these results support REM’s core notion of differentiation (for both item and source information) as well as the concept of local matching proposed by the present extension.