Importunate, a.
Etymology: [See Importune.]
1. Troublesomely urgent; unreasonably solicitous; overpressing in request or demand; urgent; teasing; as, an impotunate petitioner, curiosity. Whewell.
2. Hard to be borne; unendurable. [R.] Donne. -- Im*por"tu*nate*ly, adv. -- Im*por"tu*nate*ness, n.
Shades of meaning
Fernald has no entry of its own for importunate; he lists it under eager.
He lists it without comment; the entries above explain its neighbors.