  We analyze oriented event-shapes in the context of Soft-Collinear Effective
Theory (SCET) and in Fixed-Order perturbation theory. Oriented event-shapes are
distributions of event-shape variables which are differential on the angle
theta_T that the thrust axis forms with the electron-positron beam. We show
that at any order in perturbation theory and for any event shape, only two
angular structures can appear: F_0 = 3/8(1 + cos^2 theta_T) and F_1 = (1 -
3cos^2 theta_T). When integrating over theta_T to recover the more familiar
event-shape distributions, only F_0 survives. The validity of our proof goes
beyond perturbation theory, and hence only these two structures are present at
the hadron level. The proof also carries over massive particles. Using SCET
techniques we show that singular terms can only arise in the F_0 term. Since
only the hard function is sensitive to the orientation of the thrust axis, this
statement applies also for recoil-sensitive variables such as Jet Broadening.
We carry out resummation at N3LL of singular terms for Thrust, Heavy-Jet Mass,
the sum of the Hemisphere Masses and C-parameter. We also compute the
Fixed-Order distributions for these event-shapes at O(as) analytically and at
O(as^2) with the program Event2.
