The steady-state chemical composition of the In/Au alloy nanoparticles (NPs) during isothermal growth of Au-assisted InAs and InP nanowires (NWs) is different for the two materials. Therefore, when switching from one material to the other, to grow axial NW heterostructures, transient effects dominate during the time period of the NP reconfiguration. As a consequence, the precise control of the thickness of thin InP and InAs segments, which is fundamental for the realization of quantum dot (QD) structures and superlattices, can be very challenging. In this work, we present a study of the thickness/diameter dependence of two InP barriers and of the InAs short segment in between (QD), inserted into InAs NWs grown by means of Au-assisted chemical beam epitaxy. We found a broad variability of the InP segment thickness within the same as-grown sample, resulting in InAs NWs with asymmetric and non-homogeneous InP barriers. We explain the results by considering the NP reconfiguration dynamics which dominates at the early stages of the growth in both growth sequences. Moreover, we propose a strategy to control the growth rate and the dynamics of the barriers, by forcing the NP reconfiguration before starting the InP growth. This allows for the realization of InAs/InP NW heterostructures of different diameters, all having symmetric InP barriers with well controlled thickness, which are crucial parameters for the realization of advanced electronic quantum devices.