The block decoupling problem by admissible dynamic precompensation for LTI systems is considered. Admissibility refers to the preservation of the class of controlled output trajectories, i.e. functional output controllability is concerned, which is more demanding than just pointwise output controllability. This problem has been solved by Hautus and Heyman, within a transfer function matrix approach. Different new equivalent solvability conditions in terms of controllability subspaces, transfer function matrices or matrix pencils are given. One of these conditions (expressed in the input space) is at the origin of new necessary and sufficient conditions for block decoupling by general precompensation (possibly non admissible and nonsquare), in the wider sense of Basile and Marro.