To reduce material and processing costs of commercial permanent magnets and to attempt to fill the empty niche of energy products, 10-20 MGOe, between low-flux (ferrites, alnico) and highflux (Nd2Fe14B-and SmCo5-type) magnets, we report synthesis, structure, magnetic properties and modeling of Ta, Cu and Fe substituted CeCo5. Using a self-flux technique, we grew single crystals of I-Ce15.1Ta1.0Co74.4Cu9.5, II-Ce16.3Ta0.6Co68.9Cu14.2, III-Ce15.7Ta0.6Co67.8Cu15.9, IV-Ce16.3Ta0.3Co61.7Cu21.7 and V-Ce14.3Ta1.0Co62.0Fe12.3Cu10.4. X-ray diffraction analysis (XRD) showed that these materials retain a CaCu5 substructure and incorporate small amounts of Ta in the form of "dumb-bells", filling the 2e crystallographic sites within the 1D hexagonal channel with the 1a Ce site, whereas Co, Cu and Fe are statistically distributed among the 2c and 3g crystallographic sites. Scanning electron microscopy, energy dispersive X-ray spectroscopy (SEM-EDS) and scanning transmission electron microscopy (STEM) examinations provided strong evidence of the single-phase nature of the as-grown crystals, even though they readily exhibited significant magnetic coercivities of ∼1.6-∼1.8 kOe caused by Co-enriched, nano-sized, structural defects and faults that can serve as pinning sites. Heat treatments at 1040 • C for 10 h and a hardening at 400 • C for 4 h lead to the formation of a so-called "composite crystal" with a bimodal microstructure that consists of a Tapoor matrix and Ta-rich laminal precipitates. Formation of the "composite crystal" during the heat treatment creates a 3D array of extended defects within a primarily single grain single crystal, which greatly improves its magnetic characteristics. Possible causes of the formation of the "composite crystal" may be associated with Ta atoms leaving matrix interstices at lower temperatures and/or matrix degradation induced by decreased miscibility at lower temperatures. Fe strongly improves both the Curie temperature and magnetization of the system resulting in (BH)max.≈13 MGOe at room temperature.