  This article sheds new light on the problem of cosmological reduction in Loop
Quantum Gravity. We critically analyze Quantum Reduced Loop Gravity -- an
attempt to extract the cosmological sector of the full theory. We reconsider
the reduction procedure applied to the states of the kinematical Hilbert space,
developing a comparative analysis with previous efforts in the literature. We
show that the constraints of the model were formerly instantiated in an
inconsistent fashion, leading to an overconstrained dynamics and an ill-defined
Hilbert space. We then scrutinize alternative implementations of
symmetry-reduction. While remaining unaffected by the shortcomings encountered
in Quantum Reduced Loop Gravity, these latter procedures bridge the gap between
the full theory and former endeavors in Loop Quantum Cosmology.
