Internal stiffness matrices for square and cubic reference p-elements with the tensor products of integrated Legendre polynomials for coordinate functions are considered. The powers io In hp-adaptive computations, discretizations should be such that for each finite element, each face and each edge orders of the subspaces of the internal polynomials (on the respective subset of the reference element) can be different. An efficient DD (domain decomposition) preconditioner for the hierarchical hp discretizations, possessing the pointed out properties, of 3-d elliptic 2-nd order equations is presented. It is based on the fast inexact solvers for the internal Dirichlet problems on finite elements and faces and wire basket preconditioning. We also justify the use of inexact solvers for prolongations inside elements from the inter-element boundary and from the wire basket on faces. The DD preconditioner is almost optimal with respect to p in the total arithmetical cost and provides a high level of paralleli