The Army has been accused of failing in its handling of new recruits and allowing bullying to go unreported, in a report by MPs.
Defence secretary Geoff Hoon was criticised for the Deepcut deaths
The Commons Defence Select Committee suggested creating an independent complaints panel and looked at raising the minimum recruitment age to 18.
The inquiry was sparked by the deaths of four recruits at Deepcut barracks in Surrey between 1995 and 2002.
Their families said after the report they still wanted a public inquiry.
The report said: "In the past, insufficient weight has been given to the issue of bullying, which led to a tolerance of, or at least insufficient action being taken against, bullying."
THE DEAD DEEPCUT SOLDIERS
(Clockwise from top left):
Sean Benton, 20, Hastings, East Sussex
James Collinson, 17, Perth
Geoff Gray, 17, Seaham, Co Durham
Cheryl James, 18, Llangollen, north Wales
Jim Collinson - who lost his 17-year-old son James - said that, had they known what the training regime was like, they would not have let their son join up at such a young age.
In the lengthy report, the committee said the armed forces perceived victims of bullying as "weak", and needed a change in culture.
Counsellors should be available at training centres, as recruits were often "reluctant to discuss their concerns with the chain of command", it added.
Members also pushed the MoD to "bolster" vetting procedures for civilian and military instructors, to ensure cases like that of Leslie Skinner - convicted in 2004 of indecent assaults at Deepcut - did not happen again.
A new independent complaints body should replace the current system, under which officers handle bullying complaints, it added.
The panel would have retrospective powers, allowing it to examine the Deepcut cases, as well as a series of deaths at the Catterick barracks in Yorkshire.
The report, which followed a year-long investigation, looked at all the armed services but was particularly critical of the Army.
Armed Forces minister Adam Ingram said he had suffered "disquiet" over what happened at Deepcut and that there had been mistakes in the investigations of the deaths.
He said the government would look at the issue of raising the age of recruitment to 18, but he did not "think it was necessarily the best approach".
Geoff Gray, whose 17-year-old son, also called Geoff, died at Deepcut, welcomed the report but questioned whether it went far enough.
The MoD admitted there were "weaknesses" in some parts of the training organisation but said a "far-reaching" review of training in the forces was being undertaken.
In a statement the ministry vowed it wanted "to get our duty of care absolutely right".
Tory defence spokesman Gerald Howarth said the MoD had failed to respond to a series of internal reports.
He added: "We do not believe that the establishment of an independent commission is the answer because it risks further eroding the vital importance of the chain of command."
Lib Dem defence spokesman Paul Keetch, while regretting the lack of support for a public inquiry, welcomed the report's adoption of his party's policy of establishing an independent military complaints commission to deal with bullying and harassment.