Sensible; not flighty.
1869. The wanderers were right, and the heads of the same were level.Mark Twain, The Innocents Abroad, ch. xl.
1870. To tell a woman her head is level is apparently a compliment in America.The Orchestra, Aug. 12. (N.E.D.)
1879. Brave-hearted, strong-limbed, and clear-headed, or, as they would now be called, level-headed, were these children of the Berkshire hills.A. Tourgée, A Fools Errand, p. 8. (N.E.D.) (Italics in the original.)
1882. You see, gentlemen, says Bliss, Chets head is level usually, but in the host of things he has to see to he is apt to go wrong now and then.Washington Critic, March 13.
1909. There is also the spread-eagle style into which ordinarily level-headed men will sometimes suddenly and mysteriously drop.N.Y. Evening Post, Jan. 25.