We present a route to near-perfect absorption in compact photonic-crystal (PC) structures constructed from strongly absorbing media that are typically highly reflective in bulk form. Our analysis suggests that the key underlying mechanism in such PC superabsorbers is the existence of a PC-band-edge reflectionless condition. Although the latter is by default uncharacteristic in photonic crystals, we propose here a clear recipe on how such condition can be met by tuning the structural characteristics of one-dimensional lossy PC structures. Based on this recipe, we constructed a realizable three-layer SiC-BaF2-SiC PC operating within the Reststrahlen band of SiC. We demonstrate near-perfect absorption in this prototype of total thickness smaller than π/3, where more than 90% of the impinging light is absorbed by the top deep-subwavelength layer of thickness βΌπ/1100. We believe our study will inspire new photonic-crystal-based designs for extreme absorption harnessing across the electromagnetic spectrum.