  Dressed Gluon Exponentiation (DGE) is used to calculate the thrust and the
heavy-jet mass distributions in e+e- annihilation in the two-jet region. We
perform a detailed analysis of power corrections, taking care of the effect of
hadron masses on the measured observables. In DGE the Sudakov exponent is
calculated in a renormalization-scale invariant way using renormalon
resummation. Neglecting the correlation between the hemispheres in the two-jet
region, we express the thrust and the heavy-jet mass distributions in terms of
the single-jet mass distribution. This leads to a simple description of the
hadronization corrections to both distributions in terms of a single shape
function, whose general properties are deduced from renormalon ambiguities.
Matching the resummed result with the available next-to-leading order
calculation, we get a good description of the thrust distribution in a wide
range, whereas the description of the heavy-jet mass distribution, which is
more sensitive to the approximation of the phase space, is restricted to the
range rho_H<1/6. This significantly limits the possibility to determine alpha_s
from this observable. However, fixing alpha_s by the thrust analysis, we show
that the power corrections for the two observables are in good agreement.
