We prove complete controllability for rotational states 
of an asymmetric top molecule belonging to degenerate 
values of the orientational quantum number M. Based on this 
insight, we construct a pulse sequence that energetically 
separates population initially distributed over degenerate 
M-states, as a precursor for orientational purification. 
Introducing the concept of enantio-selective controllability, 
we determine the conditions for complete enantiomer-specific 
population transfer in chiral molecules and construct pulse 
sequences realizing this transfer for population initially 
distributed over degenerate M-states. This degeneracy 
presently limits enantiomer-selectivity for any initial 
state except the rotational ground state. Our work thus 
shows how to overcome an important obstacle towards separating, 
with electric fields only, left-handed from right-handed 
molecules in a racemic mixture.