The drift diffusion model (Ratcliff, 1978) is widely used to model binary decision-making. In this model, evidence for the two alternatives is integrated over time until it hits a decision boundary leading to a reaction. The drift diffusion model fits many psychophysical data well and is mathematically tractable for analysis. We investigated whether this model could explain feature fusion. To this end, we presented two verniers briefly flashed in a sequence. The resulting percept is a vernier of intermediate offset, because the offset fuse. In a speeded 2AFC task, we asked subjects to report the direction of fused verniers offsets. Crucially, the reported more strongly determined by the second vernier offset than the first. The drift diffusion model cannot explain this result because accumulated evidence reaches the threshold for the first vernier before the second vernier can influence the decision. We show that a biologically plausible two-stage model is capable of reproducing the empirical data. In the first stage, evidence is integrated and buffered. In the second stage, this integrated information is fed to a decision process, modeled by a biologically plausible neural network for decision-making (Wong & Wang, 2006). The success of this model suggests that information is integrated for substantial time before a decision is made.