In this work we study the kinetics of cesium lead halide perovskite nanoparticle (NP) growth; the focusing and de-focusing of the NP size distribution. Cesium lead halide perovskite NPs are considered to be attractive materials for optoelectronic applications. Understanding the kinetics of the formation of these all-inorganic perovskite NPs is critical for reproducibly and reliably generating large amounts of uniformly sized NPs. Here we investigate different growth durations for CsPbI3 and CsPbBr3 NPs, tracking their growth by high-resolution transmission electron microscopy and size distribution analysis. As a result, we are able to provide a detailed model for the kinetics of their growth. It was observed that the CsPbI3 NPs exhibit focusing of the size distribution in the first 20 seconds of growth, followed by de-focusing over longer growth durations, while the CsPbBr3 NPs show de-focusing of the size distribution starting from the beginning of the growth. The monomer concentration is depleted faster in the case of CsPbBr3 than in the case of CsPbI3, due to faster diffusion of the monomers, which increases the critical radius and results in de-focusing of the population. Accordingly, focusing is not observed within 40 seconds of growth in the case of CsPbBr3. This study provides important knowledge on how to achieve a narrow size distribution of cesium lead halide perovskite NPs when generating large amounts of these promising, highly luminescent NPs.