Abstract:  We consider an equidistant array of disjoint potential wells in $\mathbb{R}^{\nu}$, $\nu \geq 2$, built over a straight line, and show that, under a restriction on the potential support aspect ratio, a perturbation consisting of longitudinal shifts of a finite number of them preserving the disjointness gives rise to a nonempty discrete spectrum below the threshold of the lowest spectral band.