  The ambiguity of the Weitzenb\"ock connection and the meaning of torsion in
teleparallel theories are investigated. A new postulate is added to
teleparallel theories in order to remove the ambiguity and the inconsistencies
in the calculation of the gravitational energy-momentum tensor and the like. In
addition to the known restrictions on the spatial triad, it is shown that some
restrictions on the congruence used to build the frame must also be imposed.
Nevertheless, no restriction is imposed on a particular observer's worldline.
The postulate and the restriction presented in this article are used to define
what will be called here an ideal frame. This definition is applied to the
Schwarzschild and the pp-wave spacetimes in the context of the Teleparallel
Equivalent of General Relativity. In both cases, the results are very appealing
and consistent; this includes the impossibility of making the gravitational
energy density vanish along the accelerated observers' worldlines used here.
Two promising interpretations for the Weitzenb\"ock torsion are presented and
discussed in detail. The possibility of having a well defined concept of an
absolute vacuum in teleparallel theories is also discussed. Finally, some
possible solutions to well-known problems of the f(T) theories are proposed.
