This paper is devoted to H₂-optimization of linear time invariant (LTI) systems with scalar controls and external disturbances. It is supposed that the intensities of control actions are not given initially for all channels of control. In conformity, a joined problem of H₂-optimal synthesis is posed including allocation of control actions. To solve this problem, a specific spectral approach in frequency domain is developed based on polynomial factorization. Some theoretical details are discussed and numerical algorithm is proposed for practical implementation of this approach, which allows to increase a computational efficiency of synthesis. Applicability and effectiveness of the proposed approach are illustrated by numerical example.