A bad-tempered over (6)

I believe the answer is:

across

'over' is the definition.
('across' can be a synonym of 'over')

'a bad-tempered' is the wordplay.
'bad-tempered' becomes 'cross' ('cross' can be a synonym of 'bad-tempered').
'a'+'cross'='ACROSS'

(Other definitions for across that I've seen before include "Clue with solution not going in the direction of this one!" , "Astride" , "written like this?" , "sort of clue?" , "ax" .)

I've seen this clue in The Telegraph and The Guardian.

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