Synonyms for Offhanded (same or very similar meaning)
WordNet sense 1 (with little or no preparation or forethought):
ad-lib, extemporaneous, extempore, impromptu, off-the-cuff, offhand, unrehearsed, extemporary, offhand
WordNet sense 2 (without preparation; not prepared for):
unprepared
WordNet sense 3 (without previous thought or preparation):
offhandedly
WordNet sense 4 (marked by lack of attention or consideration or forethought or thoroughness; not careful):
careless
From the ODE community, based on WordNet
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