A dictionary of Confusable Phrases: More Than 10,000 Idioms and Collocations

Note: 
The expression does not correlate in meaning with the
phrase under wraps— used of smth. kept secret: The investiga-
tion apparently cleared the officers of any wrongdoing but the
details are still under wraps.
undercover —(attrib.) 
1
. situated under the roof; sheltered
from the elements: Undercover storage for vehicles is available
for either short or long term requirements. 2. (of methods,
agents, etc.) underground; secret: The menace of recruitment
to undercover prostitution on a large scale cannot be ignored.
under ground • underground
under ground —below the surface of the ground: Attending
college while working under ground is not a dream come true,
but conductors are well paid.
underground —(attrib.)
1
. situated or taking place below the
surface of the ground: This difference could have been the
result of the unaccounted for flow of underground waters into
the lake. 2. (of a political movement, etc.) concealed and acting
in secret : Until recently people suspected of underground
activity had been arrested and court-martialed. 3. separate
from a prevailing social or artistic environment: Although this
form of underground art rarely makes it into the museums, it
has attracted huge interest in recent years.
under heaven • under the sky
under heaven —
1
. on earth; in the world: You travel for
twenty miles over one of the most unfortunate, desolate coun-
tries under heaven. 2. is used to emphasize an interrogative
sentence: And why under heaven should one write a history
of anything — even a tramp dog!— without a sense of humor!
under the sky —
1
. (also: under the open sky) in the open air;
not inside a house or building: I will sleep under the sky rather
than stay in the city for another night. 2. = under heaven 
1
:
Am I deceived, I who have known more liars than any man
under the sky?