Sliding-window aggregation is a widely-used approach for extracting insights from the most recent portion of a data stream. The aggregations of interest can usually be cast as binary operators that are associative, but they are not necessarily commutative nor in-vertible. Non-invertible operators, however, are difficult to support efficiently. The best published algorithms require O(log n) aggregation steps per window operation, where n is the sliding-window size at that point. For a FIFO window, this can be improved to 0(1) on average by using two aggregation stacks. This paper presents DABA, a novel algorithm for aggregating FIFO sliding windows that significantly improves upon these time bounds. DABA requires only 0(1) aggregation steps per operation in the worst case (not just on average). As such, DABA asymptotically improves the performance of sliding-window aggregation without restricting the operator to be invertible. Our experimental results demonstrate that these theoretical improvements hold in practice. DABA is a substantial improvement over the state of the art in terms of both latency and throughput.