Mars and the Moon are envisaged as major destinations of future space exploration missions in the upcoming decades. Imaging LIDARs are seen as a key enabling technology in the support of autonomous guidance, navigation and control operations, as they can provide very accurate, wide range, high-resolution distance measurements as required for the exploration missions. Imaging LIDARs can be used at critical stages of these exploration missions, such as descent and selection of safe landing sites, rendezvous and docking manoeuvres, or robotic surface navigation and exploration. Despite these devices have been commercially available and used for long in diverse metrology and ranging applications, their size, mass and power consumption are still far from being suitable and attractive for space exploratory missions. Here, we describe a compact Single-Pixel Imaging LIDAR System that is based on a compressive sensing technique. The application of the compressive codes to a DMD array enables compression of the spatial information, while the collection of timing histograms correlated to the pulsed laser source ensures image reconstruction at the ranged distances. Single-pixel cameras have been compared with raster scanning and array based counterparts in terms of noise performance, and proved to be superior. Since a single photodetector is used, a better SNR and higher reliability is expected in contrast with systems using large format photodetector arrays. Furthermore, the event of failure of one or more micromirror elements in the DMD does not prevent full reconstruction of the images. This brings additional robustness to the proposed 3D imaging LIDAR. The prototype that was implemented has three modes of operation. Range Finder: outputs the average distance between the system and the area of the target under illumination; Attitude Meter: provides the slope of the target surface based on distance measurements in three areas of the target; 3D Imager: produces 3D ranged images of the target surface. The implemented prototype demonstrated a frame rate of 30 mHz for 16x16 pixels images, a transversal (xy) resolution of 2 cm at 10 m for images with 64x64 pixels and the range (z) resolution proved to be better than 1 cm. The experimental results obtained for the "3D imaging" mode of operation demonstrated that it was possible to reconstruct spherical smooth surfaces. The proposed solution demonstrates a great potential for: miniaturization; increase spatial resolution without using large format detector arrays; eliminate the need for scanning mechanisms; implementing simple and robust configurations.