Extreme nanowires (ENs) represent the ultimate class of crystals: They are the smallest possible periodic materials. With atom-wide motifs repeated in one dimension (1D), they offer a privileged perspective into the physics and chemistry of low-dimensional systems. Single-walled carbon nanotubes (SWCNTs) provide ideal environments for the creation of such materials. Here we present a comprehensive study of Te ENs encapsulated inside ultranarrow SWCNTs with diameters between 0.7 nm and 1.1 nm. We combine state-of-the-art imaging techniques and 1D-adapted ab initio structure prediction to treat both confinement and periodicity effects. The studied Te ENs adopt a variety of structures, exhibiting a true 1D realization of a Peierls structural distortion and transition from metallic to insulating behavior as a function of encapsulating diameter. We analyze the mechanical stability of the encapsulated ENs and show that nanoconfinement is not only a useful means to produce ENs but also may actually be necessary, in some cases, to prevent them from disintegrating. The ability to control functional properties of these ENs with confinement has numerous applications in future device technologies, and we anticipate that our study will set the basic paradigm to be adopted in the characterization and understanding of such systems.