The aim of this work is to determine the laser powder bed fusion (LPBF) processability window for the fairly weldable Inconel 939 (IN939) alloy using pulsed wave (PW) laser emission. With that goal, a design of experiments strategy was put in place with the aim of finding out the laser power, scan speed and hatch distance parameters that would render the lowest defect density. Also, a combination of characterization techniques, including optical microscopy, electron backscattered diffraction, and transmission electron microscopy was utilized to examine the microstructure of as-built and heat treated samples at different length scales. Finally, mechanical tests were carried out at temperatures ranging from room temperature to 950 °C and quasi-static strain rates in order to compare the mechanical performance of the additively manufactured specimens with that of cast samples. This work demonstrates that it is possible to process IN939 by PW LPBF with densities exceeding 99.5% and that a relatively large flexibility in microstructural design is allowed within the optimum processability window. In particular, both polycrystalline samples with weak textures and irregularly shaped grains, as well as columnar structures with relatively strong <001> fibers can be manufactured. It is shown that, using the standard post-processing heat treatment, the mechanical behavior of PW LPBF Inconel 939 specimens is superior to that of cast specimens at T ≤ 700 °C due to a strong Hall-Petch effect, but that pronounced softening takes place at T > 700 °C due to an enhanced role of diffusion-based processes. This study provides guidelines for the manufacturing of PW LPBF IN939 specimens with superior mechanical behavior at a wide range of temperatures.