As previously proposed in Simpson and Visser [J. Cosmol. Astropart. Phys. 02 (2019) 042], Mazza et al. [J. Cosmol. Astropart. Phys. 04 (2021) 082], Franzin et al. [J. Cosmol. Astropart. Phys. 07 (2021) 036], and Lobo et al. [Phys. Rev. D 103, 084052 (2021), the ``black bounce'' spacetimes are an interesting type of globally regular modifications of the ordinary black holes (such as the Kerr-Newman geometry and its particular cases) which generically contain a spacetime singularity (usually of the curvature type) at their center. To transforms a static, spherically symmetric and asymptotically flat black hole (SSS-AF-BH) geometry regular everywhere except its center of symmetry $r=0$ (where $r$ stands for the ``areal radius'' of the two-dimensional spheres of symmetry) and with (outer) event horizon at $r={r}_{h}>0$, into a black bounce spacetime, is to simply replace $r$ with $\sqrt{{\ensuremath{\rho}}^{2}+{a}^{2}}$ and $dr$ with $d\ensuremath{\rho}$, being $\ensuremath{\rho}$ a new radial coordinate, and $a$ is some real constant nonzero. As long as ${r}_{h}=\sqrt{{\ensuremath{\rho}}_{h}^{2}+{a}^{2}}>|a|$, the result is a globally regular (or singularity-free) black hole spacetime (called black bounce) where the singularity that occurs in the ordinary SSS-AF-BH geometry at $r=0$ now in the transformed geometry turns into a regular spacetime region determined by the two-dimensional spheres of symmetry of radius $|a|$, while the areal radius $\sqrt{{\ensuremath{\rho}}^{2}+{a}^{2}}$ always remains positive for all $\ensuremath{\rho}\ensuremath{\in}(\ensuremath{-}\ensuremath{\infty},\ensuremath{\infty})$ and has a minimum at $\ensuremath{\rho}=0$ given by $|a|$. Hence, in the transformed spacetime, the areal radius has a minimum, decreasing before and increasing after this minimum (defining two SSS-AF regions that bounce). In this work we will present several black-bounces exact solutions of General Relativity. Among them is a novel type of black-bounce solution, which in contrast to the Simpson-Visser type {[Simpson and Visser, J. Cosmol. Astropart. Phys. 02 (2019) 042], [Mazza et al., J. Cosmol. Astropart. Phys. 04 (2021) 082], [Franzin et al., J. Cosmol. Astropart. Phys. 07 (2021) 036], [Lobo et al., Phys. Rev. D 103, 084052 (2021)]}, does not have the Ellis wormhole metric as a particular case. The source of these solutions is linear superposition of phantom scalar fields and nonlinear electromagnetic fields.