  We make progress towards resummation of power-suppressed logarithms in dijet
event shapes such as thrust, which have the potential to improve high-precision
fits for the value of the strong coupling constant. Using a newly developed
formalism for Soft-Collinear Effective Theory (SCET), we identify and compute
the anomalous dimensions of all the operators that contribute to event shapes
at order $1/Q^2$. These anomalous dimensions are necessary to resum
power-suppressed logarithms in dijet event shape distributions, although an
additional matching step and running of observable-dependent soft functions
will be necessary to complete the resummation. In contrast to standard SCET,
the new formalism does not make reference to modes or $\lambda$-scaling. Since
the formalism does not distinguish between collinear and ultrasoft degrees of
freedom at the matching scale, fewer subleading operators are required when
compared to recent similar work. We demonstrate how the overlap subtraction
prescription extends to these subleading operators.
