Fact finders in legal trials often need to evaluate a mass of weak, contradictory and ambiguous evidence. There are two general ways to accomplish this task: by holistically forming a coherent mental representation of the case, or by atomistically assessing the probative value of each item of evidence and integrating the values according to an algorithm. Parallel constraint satisfaction models of cognitive coherence posit that a coherent mental representation is created by discounting contradicting evidence, inflating supporting evidence and interpreting ambivalent evidence in a way coherent with the emerging decision. This leads to inflated support for whichever hypothesis the fact finder accepts as true. Using a Bayesian network to model the direct dependencies between the evidence, the intermediate hypotheses and the main hypothesis, parameterised with (conditional) subjective probabilities elicited from the subjects, I demonstrate experimentally how an atomistic evaluation of evidence leads to a convergence of the computed posterior degrees of belief in the guilt of the defendant of those who convict and those who acquit. The atomistic evaluation preserves the inherent uncertainty that largely disappears in a holistic evaluation. Since the fact finders’ posterior degree of belief in the guilt of the defendant is the relevant standard of proof in many legal systems, this result implies that using an atomistic evaluation of evidence, the threshold level of posterior belief in guilt required for a conviction may often not be reached.