Kenneth G. Wilson (1923). The Columbia Guide to Standard American English. 1993.
undue (adj.), unduly (adv.)
Undue means either not required, unnecessary, as in Her haste was wholly undue and unwarranted, or excessive, improper, as in His undue influence over the boy caused much suffering. Unduly means unnecessarily or excessively, as in The family were unduly alarmed at his absence. Despite some purist suggestions that not to feel undue alarm and not to be unduly alarmed may be redundancies, they appear instead to be emphatic, hyperbolic, and Standard.