Green’s Dictionary of Slang

smooth up v.

[smooth adj. (2)]

(US campus) of a man, to attempt seduction.

[US]Phila. Inquirer 16 June n.p.: The ‘smoothie,’ a college man who has something which is difficult to describe. Whatever it is, he has it; and, the article goes on to say, ‘when one is entertaining a young lady it is always well to avoid a “smoothie,” lest he try to “smooth” ’em up’.