Cascades are a popular framework to speed up object detection systems. Here we focus on the first layers of a category independent object detection cascade in which we sample a large number of windows from an objectness prior, and then discriminatively learn to filter these candidate windows by an order of magnitude. We make a number of contributions to cascade design that substantially improve over the state of the art: (i) our novel objectness prior gives much higher recall than competing methods, (ii) we propose objectness features that give high performance with very low computational cost, and (iii) we make use of a structured output ranking approach to learn highly effective, but inexpensive linear feature combinations by directly optimizing cascade performance. Thorough evaluation on the PASCAL VOC data set shows consistent improvement over the current state of the art, and over alternative discriminative learning strategies.