Conductance through weak constrictions in Luttinger liquids is shown to vanish with frequency omega as c(1)w(2) + c(2) omega(2/g-2), where g is a dimensionless parameter characterizing the Luttinger-liquid phase, and c(1) and c(2) are non-universal constants. The first term arises from the <<Coulomb blockade>> effect and dominates for g < 1/2, whereas the second results from eliminating high-energy modes and dominates for g > 1/2.