level-headed (adj.)

early 15c., "having an even surface," from level (n.). Meanings "lying on or constituting a horizontal surface" and "lying in the same horizontal plane" (as something else) are from 1550s. To do one's level best is U.S. slang from 1851, from level in the sense "well-aimed, direct, straight." Level playing field as a figure of equality of opportunity is from 1981. Related: Levelly.

"having a head" (of a specified kind); see head (n.).