We study the fluctuation of shape-deformation as currently implemented in MC-Glauber-like models and their consequences on the magnitude of initial-state eccentricities. We show that for both deformed and spherical colliding species, there are large fluctuations in the deformation that emerge event by event. We characterize these deformations with the ratio of the largest and smallest eigenvalues ($\lambda_1$ and $\lambda_3$) of the covariance matrix for the coordinates of the colliding nucleons. The second order initial-state eccentricity $\varepsilon_2$, shows a strong correlation with fluctuations of the ratio $\lambda_1/\lambda_3$ for ultra central collisions; the conditional mean $E(\varepsilon_2|(\lambda_1/\lambda_3)_1+(\lambda_1/\lambda_3)_2)$ varies by O(100\%) for 0-1\% Pb+Pb collisions. However, the number of participants, as well as the higher-order eccentricities, are unmodified. We further show, via acoustic scaling, that for constrained values of $\lambda_1/\lambda_3$, $v_n/\varepsilon_n$ for ultra-central collisions, scale in the same way as for mid-central and peripheral collisions for the wealth of differential $v_n$ measurements in ultra-central collisions.