Accurate, fast, and reliable 3D perception is essential for autonomous driving. Recently, bird's-eye view (BEV)-based perception approaches have emerged as superior alternatives to perspective-based solutions, offering enhanced spatial understanding and more natural outputs for planning. Existing BEV-based 3D object detection methods, typically using an angle-based representation, directly estimate the size and orientation of rotated bounding boxes. We observe that BEV-based 3D object detection is analogous to aerial oriented object detection, where angle-based methods are known to suffer from discontinuities in their loss functions. Drawing inspiration from this domain, we propose \textbf{R}estricted \textbf{Q}uadrilateral \textbf{R}epresentation to define \textbf{3D} regression targets. RQR3D regresses the smallest horizontal bounding box encapsulating the oriented box, along with the offsets between the corners of these two boxes, thereby transforming the oriented object detection problem into a keypoint regression task. We employ RQR3D within an anchor-free single-stage object detection method achieving state-of-the-art performance. We show that the proposed architecture is compatible with different object detection approaches. Furthermore, we introduce a simplified radar fusion backbone that applies standard 2D convolutions to radar features. This backbone leverages the inherent 2D structure of the data for efficient and geometrically consistent processing without over-parameterization, thereby eliminating the need for voxel grouping and sparse convolutions. Extensive evaluations on the nuScenes dataset show that RQR3D achieves SotA camera-radar 3D object detection performance despite its lightweight design, reaching 67.5 NDS and 59.7 mAP with reduced translation and orientation errors, which are crucial for safe autonomous driving.