Object detection models are usually trained and evaluated on highly complicated, challenging academic datasets, which results in deep networks requiring lots of computations. However, a lot of operational use-cases consist of more constrained situations: they have a limited number of classes to be detected, less intra-class variance, less lighting and background variance, constrained or even fixed camera viewpoints, etc. In these cases, we hypothesize that smaller networks could be used without deteriorating the accuracy. However, there are multiple reasons why this does not happen in practice. Firstly, overparameterized networks tend to learn better, and secondly, transfer learning is usually used to reduce the necessary amount of training data. In this paper, we investigate how much we can reduce the computational complexity of a standard object detection network in such constrained object detection problems. As a case study, we focus on a well-known single-shot object detector, YoloV2, and combine three different techniques to reduce the computational complexity of the model without reducing its accuracy on our target dataset. To investigate the influence of the problem complexity, we compare two datasets: a prototypical academic (Pascal VOC) and a real-life operational (LWIR person detection) dataset. The three optimization steps we exploited are: swapping all the convolutions for depth-wise separable convolutions, perform pruning and use weight quantization. The results of our case study indeed substantiate our hypothesis that the more constrained a problem is, the more the network can be optimized. On the constrained operational dataset, combining these optimization techniques allowed us to reduce the computational complexity with a factor of 349, as compared to only a factor 9.8 on the academic dataset. When running a benchmark on an Nvidia Jetson AGX Xavier, our fastest model runs more than 15 times faster than the original YoloV2 model, whilst increasing the accuracy by 5% Average Precision (AP).