Colloidal lead halide perovskite (LHP) nanocrystals (NCs, with bright and spectrally narrow photoluminescence (PL) tunable over the entire visible spectral range, are the latest generation of semiconductor quantum dots (QDs) of immense interest as classical and quantum light sources. LHP NCs form by sub-second fast and hence hard-to-control ionic metathesis reactions, which severely limits the access to size-uniform and shape-regular NCs in the sub-10 nm range. We posit that a synthesis path comprising an intricate equilibrium between the precursor (PbBr2) and the CsPbBr3 solute for the QD nucleation may circumvent this challenge. Here, we report a room-temperature synthesis of monodisperse, isolable spheroidal CsPbBr3 QDs, size-tunable in the 3-13 nm range. The kinetics of both nucleation and therefrom temporally separated growth are drastically slowed down by the formation of transient CsPbBr3, resulting in total reaction times of up to 30 minutes. The methodology is then extended to FAPbBr3 (FA = formamidinium) and MAPbBr3 (MA = methylammonium), allowing for thorough experimental comparison and modeling of their physical properties under intermediate quantum confinement. In particular, QDs of all these compositions exhibit up to four excitonic transitions in their linear absorption spectra and we demonstrate that the size-dependent confinement energy for all transitions is independent of the A-site cation.