Since the arrests of Ian Huntley, who has been charged with murder, and Maxine Carr, who faces charges of perverting the course of justice, both have had their private lives splashed across the front pages of tabloid newspapers.
Newspapers have carried pages and pages of coverage as the case has unfolded and some newspapers have interviewed people who may be asked to give evidence at trial.
Tabloids, in particular, have ran in-depth pieces on the lives of 28-year-old Huntley and his 25-year-old girlfriend.
However, there are strict rules regarding the reporting of cases where there is a risk of prejudicing a jury against the defendants.
The police issued a statement urging editors to tone down coverage, saying that the reporting "continued to approach the boundary of what is likely to be regarded as acceptable by the trial court".
"Such continued publication is viewed by both the investigation and prosecution teams as serious since it flagrantly ignores the advice given to editors by the police and the Attorney General," the police statement said.
The move follows criticism of some British tabloids offering large cash rewards for information relating to the case, most recently by the coroner investigating the deaths.
Last year, the trial of the Leeds footballers Lee Bowyer and Jonathan Woodgate collapsed after reports appearing in the Sunday Mirror were deemed prejudicial.
However, regarding the case of Holly Wells and Jessica Chapman, leading human rights lawyer Geoffrey Robinson QC has said that there was the option of Huntley and Carr receiving trials by judge.
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