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"как можно быстро" stresses
gen.	presto possibile
как можно быстрее
gen.	ASAP; as accurate as possible (alenagorelkova); as expeditiously as possible (nerzig); as soon as possible; against time; as promptly as possible (Johnny Bravo); as rapidly as possible (Stas-Soleil)
Игорь Миг	at the earliest moment; at the earliest possible date; expeditiously
brit.	sharpish (VLZ_58)
busin.	a.s.a.p. (as soon as possible); as quickly as possible (We will respond to your e-mail as quickly as possible.)
inet.	as quickly as possible
mil., inf.	fast as can
span.-am.	pronto (популярное слово в США из мексиканского вокабуляра Val_Ships)
"как можно быстрее"
ital.	al piu presto
mil., avia.	as soon as possible
как можно быстрей
gen.	against time (jollyhamster)
как можно ... быстрее
gen.	as soon as fucking possible (skazik)

как можно быстро" : 34 phrases in 9 subjects

General	13
Informal	2
Makarov	10
Microsoft	1
Military	2
Programming	1
Scientific	1
Slang	2
Sports	2