Detection of small-sized targets is of paramount importance in many aerial vision-based applications. The commonly deployed low cost unmanned aerial vehicles (UAVs) for aerial scene analysis are highly resource constrained in nature. In this paper we propose a simple short and shallow network (SSSDet) to robustly detect and classify small-sized vehicles in aerial scenes. The proposed SSSDet is up to 4x faster, requires 4.4x less FLOPs, has 30x less parameters, requires 31x less memory space and provides better accuracy in comparison to existing state-of-the-art detectors. Thus, it is more suitable for hardware implementation in real-time applications. We also created a new airborne image dataset (ABD) by annotating 1396 new objects in 79 aerial images for our experiments. The effectiveness of the proposed method is validated on the existing VEDAI, DLR-3K, DOTA and Combined dataset. The SSSDet outperforms state-of-the-art detectors in term of accuracy, speed, compute and memory efficiency.