Since a few years, indium nitride promising properties for device applications have attracted much attention worldwide. Huge efforts are dedicated to optimize indium nitride growth. However, this growth is extremely challenging, in particular using the metal organic vapor phase epitaxy (MOVPE) technique which exhibits very low growth rates. This may explain why most of the samples available in the scientific community, which also present the best electrical properties, were grown by molecular beam epitaxy (MBE). However, up to date, no intrinsic indium nitride layer was obtained. InN epilayer crystalline quality suffers from the lack of lattice matched substrates, leading to the use of double‐step growth process. In this paper, we show that InN low lateral growth rate is a limiting parameter for efficient double‐step growth process. But, we also report that the use of CBrCl3 during InN growth enhances the lateral growth rate. To improve the growth rate along the c‐axis, we investigate alternative precursors for both nitrogen and indium species. We show that ammonia remains the best precursor, but combined with triethylindium, the growth rate increases with optimum crystalline quality. Finally, we compare MOVPE‐grown and MBE‐grown InN layers in order to understand the difference observed on the electrical properties. We show how thermal annealing can improve the MOVPE‐grown InN layers leading to similar electrical properties than reported in MBE‐grown samples. The role of ammonia as source of hydrogen is also discussed.