For any Peano continuum $X$, we construct uncountable families of rigid, $\frac{1}{n}$-rigid, and $0$-rigid continua, of which all spaces contain a homeomorphic copy of $X$. We also show that for any continuum from the mentioned uncountable families, it holds that for every sequence of continuous surjective functions from the continuum into itself, the inverse limits of such a continuum with the described sequence are homeomorphic to the continuum itself.