Coiled Carbon Nanotubes (CCNTs) are increasingly set to become a vital factor in the new generation of nanodevices and energy-absorbing materials due to their outstanding properties. In the following work, the multi-objective optimization of CCNTs is applied regarding their mechanical performances. Apart from finding the best trade-off between conflicting mechanical properties (e.g. yield stress and yield strain), the optimization enables us to find the astonishing CCNTs concerning their stretchability. To the best of our knowledge, these structures have not been recognized before, both experimentally and computationally. Several highly accurate analytical equations are derived by insights from the findings of multi-objective optimization and fitting a theoretical model to the results of Molecular Dynamics (MD) simulations. The structures resulted from optimizations are highly resilient because of two distinct deformation mechanisms depending on the dimensions of CCNTs. For small CCNTs, extraordinary extensibility is mainly contributed by buckling and nanohinge-like deformation with maintaining the inner coil diameter, whereas for large CCNTs this is accomplished by the creation of a straight CNT-like structure in the inner-edge of the CCNT with a helical graphene ribbon twisted around it. These findings would shed light on the design of CCNT based mechanical nanodevices.