From the introduction: Consider the random Schrödinger operator on \(\mathbb R^{d}\), \(H_{\varepsilon}=-\Delta +V=H^{o}+V\) with the potential \(V=V_{\varepsilon}(x)=\sum _{j\in Z^{d}} \varepsilon_{j}\varphi (x-j).\) Here \(\varepsilon_{j}\in \{ 0,1\}\) are independent and \(\varphi\) is a smooth compactly supported function satisfying \(0\leq \varphi \leq 1\) and \(\text{ supp}\;\varphi \subset B(0,1/10)\). Clearly \(\inf \text{ Spec}\; H_{\varepsilon}=0\) a.s. Our main result is the following Theorem. At energies near the bottom of the spectrum \((E>0, E\approx 0)\), \(H_{\varepsilon}\) displays spectral localization a.s. in \(\varepsilon\). By spectral localization we mean point spectrum with exponentially decaying eigenfunctions.