Ft Cryptic

[oldham1]

Composed number (4) -o- -

Still half done on the inside - turn it over for a minute (5) t-e- -

A city organisations wanton (8) - - - -o- - -

[Mamyalynne]

Cool

Teeny

Anybody's

[Lie-in King]

27d Cool (number; song; themed)
25d Teeny - '(do)ne' (half, inside) 'yet' (still) (all turned over)
30a Anybody's - a N(ew) Y(ork) body's (organisation's)

[oldham1]

Many thanks to all