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Colloidal nanocrystals (NCs) of fully inorganic lead halide perovskites (LHPs) are the latest generation of quantum-dot materials with compelling optical characteristics. Favored by the nearly regular cubic shape of NCs, they readily self-organize into highly ordered supercrystals (SCs) that have been stimulating in-depth investigation of uncommon collective properties at the fundamental level. Herein, we explore LHP NC SCs formed in colloidal suspensions and as solid materials, without any prior rigorous NC size-selection process. The spontaneous self-organization manifests itself in synchrotron wide-angle X-ray total scattering (WAXTS) measurements of randomly oriented ensembles of SCs by virtue of the substructure in the 100(c) peak (in cubic notation). By developing atomistic models of SCs, we find an evidence that, in spite of the initial NCs size polydispersity (up to 20%), SCs of CsPbBr3 and CsPbBr1.5I1.5 NCs form through a size segregation process. The SCs exhibit high spatial structural coherence, that is, crystallographic alignment between NCs, along two and three directions, a degree of orientational order (the SCs mosaicity) below 2 degrees, and coherent sizes on the order of tens of nanometers. In situ coupled photoluminescence (PL) and WAXTS experiments evidence pronounced electronic coupling between NCs in SCs, seen as an ca. 50-70 meV red-shifted emission in dried samples compared to the corresponding dilute solution of NCs. ISSN:0897-4756