Making decisions often requires the integration of multiple pieces of information that may become available at different times. An extensive body of research has investigated the neural mechanisms underpinning evidence accumulation in tasks where information is continuously available, but less is known about how humans make decisions based on temporally separate samples. Here, we ran two electroencephalography (EEG) experiments using a modified version of the standard Random Dot Kinematogram (RDK). In our tasks (N = 22, N = 21), two pulses of evidence were presented separated by "gaps" of varying duration. Our goal was to investigate 1) whether and how people integrate the two pulses across various gap durations, and 2) how a prominent EEG marker of evidence accumulation, the centroparietal positivity (CPP), participates in such a task. Behavioural analysis confirmed that both pulses inform choice, but pulse 2 was discounted to a degree that depended on a complex interaction between coherence and gap duration. Accuracy tended to benefit from longer gaps when both pulses were strong, but suffered from them when both pulses were weak, suggestive of a bounded accumulation process for pulse 1 that could inform a process for pulse 2. Behavioural sensitivity to both pulses was further modulated by attentional fluctuations, as measured by occipital alpha power. Consistent with the two-process account, the CPP did not sustain during the gap, and it not only scaled with motion coherence following pulse 1 but was also influenced by both the first and second pulse’s coherence following pulse 2.