The main obstacle for obtaining fast domain decomposition solvers for the spectral element discretizations of the 2-nd order elliptic equations was absence of fast solvers for the internal problems on subdomains of decomposition and their faces. It was shown by Korneev/Rytov (2005) that such solvers can be derived on the basis of the specific interrelation between the stiffness matrices of the spectral and hierarchical $p$ reference elements. The coordinate polynomials of the latter are produced by the tensor products of the integrated Legendre's polynomials. This interrelation allows to apply to the spectral element discretizations fast solvers which in some basic features are quite similar to those developed for the discretizations by the hierarchical elements. Using these facts, we present the almost optimal in the arithmetical cost domain decomposition preconditioner-solver for the spectral element discretizations of the 2-nd order elliptic equations in 3-$d$ domains.