A showerhead used for dispensing gas over a wafer in chemical vapor deposition (CVD), especially for CVD of metals. The patterns of holes is tailored to compensate for thermal and other effects, in particular by increasing the density of holes toward the periphery of the wafer in three or more zones. Such a variable pattern is particularly useful for liquid precursors that are atomized in a carrier gas, in which case a second perforated plate in back of the showerhead face can be eliminated, thereby reducing the flow impedance and the required pressure of the liquid-entrained gas, which tends to deposit out at higher pressures. The reduce flow impedance is particularly useful for CVD of copper.