I will present a new method to determine quark masses from heavy-lightmesonmasses.The two theoretical foundations of the method are 1) thewell-known formula for heavy-light hadron masses in the heavy-quarkeffective theory, and 2) a new definition of the heavy-quark mass with anelegant treatment of the renormalon problem. Using lattice-QCD data fromthe Fermilab Lattice and MILC Collaborations, the method yields precisionon the charmed and bottom quark masses comparable to the best existingdeterminations.Using very precise quark-mass ratios, including m_c/m_sfrom this analysis, we can obtain the most precise determinations of theup-, down-, and strange-quark masses.