NTnC-like green fluorescent genetically encoded calcium indicators (GECIs) with two calcium ion binding sites were constructed using the insertion of truncated troponin C (TnC) from Opsanus tau into green fluorescent proteins (GFPs). These GECIs are small proteins containing the N- and C-termini of GFP; they exert a limited effect on the cellular free calcium ion concentration; and in contrast to calmodulin-based calcium indicators they lack undesired interactions with intracellular proteins in neurons. The available TnC-based NTnC or YTnC GECIs had either an inverted response and high brightness but a limited dynamic range or a positive response and fast kinetics in neurons but lower brightness and an enhanced but still limited dF/F dynamic range. Here, we solved the crystal structure of NTnC at 2.5 Å resolution. Based on this structure, we developed positive NTnC2 and inverted iNTnC2 GECIs with a large dF/F dynamic range in vitro but very slow rise and decay kinetics in neurons. To overcome their slow responsiveness, we swapped TnC from O. tau in NTnC2 with truncated troponin C proteins from the muscles of fast animals, namely, the falcon, hummingbird, cheetah, bat, rattlesnake, and ant, and then optimized the resulting constructs using directed molecular evolution. Characterization of the engineered variants using purified proteins, mammalian cells, and neuronal cultures revealed cNTnC GECI with truncated TnC from Calypte anna (hummingbird) to have the largest dF/F fluorescence response and fast dissociation kinetics in neuronal cultures. In addition, based on the insertion of truncated TnCs from fast animals into YTnC2, we developed fYTnC2 GECI with TnC from Falco peregrinus (falcon). The purified proteins cNTnC and fYTnC2 had 8- and 6-fold higher molecular brightness and 7- and 6-fold larger dF/F responses to the increase in Ca2+ ion concentration than YTnC, respectively. cNTnC GECI was also 4-fold more photostable than YTnC and fYTnC2 GECIs. Finally, we assessed the developed GECIs in primary mouse neuronal cultures stimulated with an external electric field; in these conditions, cNTnC had a 2.4-fold higher dF/F fluorescence response than YTnC and fYTnC2 and was the same or slightly slower (1.4-fold) than fYTnC2 and YTnC in the rise and decay half-times, respectively.