  In the past years, black holes and the fate of their singularity have been
heavily studied within loop quantum gravity. Effective spacetime descriptions
incorporating quantum geometry corrections are provided by the so-called
polymer models. Despite the technical differences, the main common feature
shared by these models is that the classical singularity is resolved by a
black-to-white hole transition. In a recent paper, we discussed the existence
of two Dirac observables in the effective quantum theory respectively
corresponding to the black and white hole mass. Physical requirements about the
onset of quantum effects then fix the relation between these observables after
the bounce, which in turn corresponds to a restriction on the admissible
initial conditions for the model. In the present paper, we discuss in detail
the role of such observables in black hole polymer models. First, we revisit
previous models and analyse the existence of the Dirac observables there.
Observables for the horizons or the masses are explicitly constructed. In the
classical theory, only one Dirac observable has physical relevance. In the
quantum theory, we find a relation between the existence of two physically
relevant observables and the scaling behaviour of the polymerisation scales
under fiducial cell rescaling. We present then a new model based on
polymerisation of new variables which allows to overcome previous restrictions
on initial conditions. Quantum effects cause a bound of a unique Kretschmann
curvature scale, independently of the relation between the two masses.
