Long-video question answering is limited by the high cost of visual tokens and by the fixed context width of current VLMs. A long-video question may require broad temporal coverage, but the answer is often supported by only a compact set of moments. To locate these moments efficiently, we propose token-budgeted Video Evidence Indexing (VEI): given a dense low-resolution Video Preview, the model constructs a compact high-resolution Evidence Set for final reasoning. We treat VEI as a policy that must jointly solve \textit{evidence localization}, which finds question-relevant moments, and \textit{budget planning}, which decides where to spend the limited high-resolution frame budget. We implement this idea with an inference pipeline: the Video Preview provides cheap global coverage, Video Evidence Indexing constructs the Evidence Set, and Answer Generation combines both inputs for final VQA. To address missing frame-level supervision, we adopt privileged self-distillation, where an answer-aware teacher guides the normal test-time policy on student-generated indexing traces. We explore previews at 1, 6, 12, and 24 visual tokens per frame, training a single policy that supports all four resolutions. Experiments show that Video Evidence Indexing improves accuracy under limited visual budgets, and self-distillation further improves both QA accuracy and temporal evidence localization.

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