The present invention provides aqueous, epoxy-based sizing compositions for carbon fibers. The size composition incorporates highly functionalized film forming epoxy novolac phenolic resins in combination with highly functionalized sulfonated polyesters having high Tg characteristics, sulfonate equivalent weights in the range from 2000 to 20,000 and number average molecular weights in the range from about 1000 to about 100,000. The present invention also provides corresponding sized carbon fibers and fiber-reinforced matrices.