  Lie-Poisson gauge formalism provides a semiclassical description of
noncommutative $U(1)$ gauge theory with Lie algebra type noncommutativity.
Using the Dirac approach to constrained Hamiltonian systems, we focus on a
class of Lie-Poisson gauge models, which exhibit an admissible Lagrangian
description. The underlying noncommutativity is supposed to be purely spatial.
Analysing the constraints, we demonstrate that these models have as many
physical degrees of freedom as there are present in the Maxwell theory.
