Recently, two-stage Deformable DETR introduced the query-based two-stage head, a new type of two-stage head different from the region-based two-stage heads of classical detectors as Faster R-CNN. In query-based two-stage heads, the second stage selects one feature per detection processed by a transformer, called the query, as opposed to pooling a rectangular grid of features processed by CNNs as in region-based detectors. In this work, we improve the query-based head by improving the prior of the cross-attention operation with anchors, significantly speeding up the convergence while increasing its performance. Additionally, we empirically show that by improving the cross-attention prior, auxiliary losses and iterative bounding box mechanisms typically used by DETR-based detectors are no longer needed. By combining the best of both the classical and the DETR-based detectors, our FQDet head peaks at 45.4 AP on the 2017 COCO validation set when using a ResNet-50+TPN backbone, only after training for 12 epochs using the 1x schedule. We outperform other high-performing two-stage heads such as e.g. Cascade R-CNN, while using the same backbone and while being computationally cheaper. Additionally, when using the large ResNeXt-101-DCN+TPN backbone and multi-scale testing, our FQDet head achieves 52.9 AP on the 2017 COCO test-dev set after only 12 epochs of training. Code will be released.