A DD (domain decomposition) preconditioner of almost optimal in p arithmetical complexity is presented for the hierarchical hp discretizations of 3-d second order elliptic equations. We adapt the wire basket substructuring technique to the hierarchical hp discretization, obtain a fast preconditioner-solver for faces by K-interpolation technique and show that a secondary iterative process may be efficiently used for prolongations from faces. The fast solver for local Dirichlet problems on subdomains of decomposition is based on our earlier derived finite-difference like preconditioner for the internal stiffness matrices of p-finite elements and fast solution procedures for systems with this preconditioner, which appeared recently. The relative condition number, provided by the DD preconditioner under consideration, is O((1 + log p)^3.5) and its total arithmetic cost is O((1 + log p)^1.75[(1 + log p)(1 + log(1 + log p))p³R + pR²]), where R is the number of finite elements. The term pR² is due to the solver for the wire basket subsystem. We outline, how the cost of this component may be reduced to O(pR). The presented DD algorithms are highly parallelizable.