Let G be an infinite compact abelian group and let Ꞅ denote its dual group. A borel measure µ on G is called Lorentz-improving if there existe p, q1, and q2, where 1 < p < ꝏ and 1 ≤ q1 ≤ q2 ≤ ꝏ, such that µ * L (p, q2) ⊆  L (p, q1). A detailed exposition of our recent characterization of Lorentz-improving measures is presented here. In this result Lorentz-improving measures are characterized in terms of the size of the sets {ϒ ∊ Ꞅ : │ µ (ϒ) │  > ∊ } and in terms of n-fold convolution powers. This characterization is analogous to a known characterization of LP-improving measures due to Hare.