Prosecutor Andrew Edis QC told the Old Bailey that, while former News of the World and Sun editor Brooks was being questioned by police over the voicemail allegations, her husband Charlie and former NI head of security Mark Hanna tried to hide evidence.
It is claimed that security staff picked up a bin bag of material from the couple's Oxfordshire home, Jubilee Barn, before it could be searched on the day of Brooks' arrest, and that this was hidden near bins at the couple's flat in London's Chelsea Harbour.
However before the bag could be recovered, it was found by a cleaner and handed to police, the jury was told.
Mr Edis said: "The prosecution say that this whole exercise was quite complicated and quite risky and liable to go wrong, as it did.
"You only contemplate doing it for a real purpose, otherwise you are just attracting suspicion."
He added: "The only rational explanation was to hide material so police can't get it. Sometimes plans of that kind succeed.
"They must have been trying to hide something, otherwise they would have been behaving completely irrationally."
Rebekah Brooks, 45, is accused of two counts of perverting the course of justice - one with Hanna and her husband, and the second with her former personal assistant, Cheryl Carter.
It is claimed that she instructed Carter to remove seven boxes of notebooks - said to be Brooks' dating from 1995 to 2007 - from the company's archive that have "never been seen again".
Mr Edis told the nine women and three men on the jury: "Nothing like that has ever been recovered in the course of this inquiry."
Earlier the court was told that in 2011 the situation for News International became "more fevered" as the firm came under investigation by police after it handed over three emails linked to phone hacking and payment claims.
Mr Edis said: "This was a huge business for News International and for her (Brooks). There were inquiries ongoing. At all times she was of course aware that there was a police inquiry, Operation Weeting, which had in fact started when News International handed over these three emails.
"So there was always a course of justice in existence that could be perverted by hiding evidence.
"Hiding evidence was not acceptable at any time that year.
"The atmosphere, we would suggest, became even more fevered as time went on."
He added: "You can imagine the extremely anxious, if not panic-stricken approach to what was going on."
Jurors were told that a security guard was tasked with taking the bin bag to Chelsea Harbour, under the pretext of delivering pizza.
After he had dropped off the package, he sent a text message to a colleague, referencing the 1968 film Where Eagles Dare starring Clint Eastwood and Richard Burton, which said: "Broadsword calling Danny Boy. Pizza delivered and the chicken's in the pot." To which the colleague replied: "Ha, f****** amateurs. We should have done a DLB (dead letter box) or brush contact on the riverside."
Neither of the men can be named for legal reasons.
Mr Edis told the jury that the security staff agreed to log the hours for the car park drop-off as "pizza delivery", because "you cannot log the hours as 'perverting the course of justice'."
Rebekah Brooks, of Churchill, Oxfordshire; Coulson, 45, from Charing in Kent; former NotW head of news Ian Edmondson, 44, from Raynes Park, south west London; and the tabloid's ex-managing editor Stuart Kuttner, 73, from Woodford Green, Essex, all deny conspiring with others to hack phones between October 3 2000 and August 9 2006.
Former NotW and Sun editor Brooks is also accused of two counts of conspiring with others to commit misconduct in public office - one between January 1 2004 and January 31 2012 and the other between February 9 2006 and October 16 2008 - linked to alleged inappropriate payments to public officials.
She faces the two allegations of conspiracy to pervert the course of justice - one with Carter, 49, from Chelmsford in Essex, between July 6 and 9 2011; and a second with her husband, Charles Brooks, Hanna, and others between July 15 and July 19 2011.
Coulson is also facing two allegations that he conspired with former NotW royal editor Clive Goodman, 56, from Addlestone in Surrey, and other unknown people to commit misconduct in public office - between August 31 2002 and January 31 2003, and between January 31 and June 3 2005.