Decision models involving protracted temporal integration of sensory information are known to provide excellent fits to decision behaviour. However, despite the computational advantage in principle, several studies have suggested a limited role for extended integration in practice, variously finding that it is subjected to low bounds, applied over a short timeframe, or plausibly replaced by non-integration strategies such as extrema detection. Here, we probed the role of extended integration in a noiseless but difficult contrast comparison task with response choices made after viewing a long 1.6-sec stimulus in which evidence duration was manipulated unbeknownst to the subject. In behaviour-only modelling, integration (drift diffusion), and non-integration models captured accuracy improvements with evidence duration comparably well, and favoured unbounded models. On the contrary, an EEG signature of evidence accumulation showed prolonged buildup during hard trials, and an early, high-amplitude peak in rare, interleaved high-contrast trials, suggestive of both integration and a decision bound. Adding estimates of accumulator drift rate modulation, relative amplitude and buildup duration from neural data as constraints to the models, a more decisive best-fit was obtained by an integration model with high bound. Follow-up models with freely-adjustable accumulation duration produced long estimates for this duration (~1.6s). Thus, by leveraging neural data to constrain alternative behavioural models, we ruled out unbounded models and selected bounded integration as the mechanism capturing both behavior and neural features of the data. In so doing, we demonstrate the power of neurally constrained modelling to address issues of model mimicry in behavioural modelling.