Being capable of estimating the pose of uncooperative objects in space has been proposed as a key asset for enabling safe close-proximity operations such as space rendezvous, in-orbit servicing and active debris removal. Usual approaches for pose estimation involve classical computer vision-based solutions or the application of Deep Learning (DL) techniques. This work explores a novel DL-based methodology, using Convolutional Neural Networks (CNNs), for estimating the pose of uncooperative spacecrafts. Contrary to other approaches, the proposed CNN directly regresses poses without needing any prior 3D information. Moreover, bounding boxes of the spacecraft in the image are predicted in a simple, yet efficient manner. The performed experiments show how this work competes with the state-of-the-art in uncooperative spacecraft pose estimation, including works which require 3D information as well as works which predict bounding boxes through sophisticated CNNs.