Recent years witnessed progressive broadening of the practical use of 3D-printed aluminium alloy parts, in particular for specific aerospace applications where weight saving is of great importance. Selective laser melting (SLM) is an intrinsically multi-parametric fabrication technology that offers multiple means of controlling mechanical properties (elastic moduli, yield strength, and ductility) through the control over grains size, shape, and orientation. Targeted control over mechanical properties is achieved through the tuning of 3D-printing parameters and may even obviate the need of heat treatment or mechanical post-processing. Systematic studies of grain structure for different printing orientations with the help of EBSD techniques in combination with mechanical testing at different dimensional levels are the necessary first steps to implement this agenda. Samples of 3D-printable Al-Mg-Si RS-333 alloy were fabricated in three orientations with respect to the principal build direction and the fast laser beam scanning direction. Sample structure and proper-ties were investigated using a number of techniques, including EBSD, in situ SEM tensile testing, roughness measurements, and nanoindentation. The as-printed samples were found to display strong variation in Young’s modulus values from nanoindentation (from 43 to 66 GPa) and tensile tests (from 54 to 75 GPa), yield stress and ultimate tensile strength (100–195 and 130–220 MPa) in different printing orientations, and almost constant hardness of about 0.8 GPa. A further preliminary study was conducted to assess the effect of surface finishing on the mechanical performance. Surface polishing was seen to reduce Young’s modulus and yield strength but improves ductility, whereas the influence of sandblasting was found to be more controversial. The experimental results are discussed in connection with the grain morphology and orientation.