We believe that the media feeding frenzy sounding spree killings is part of the incentive of the killers. They do it for the attention, the fame, to shine a spotlight on what made them miserable.
Reducing the media coverage will reduce the fame and incentive, but we don't want to impinge on 1st amendment rights.
We want a law, mandating that all media advertising include an opt-out clause, whereby an advertiser can expect his ads to be removed, and fees reimbursed should the media cover a mass murder or spree killing.
This will serve as a check on the "if it bleeds, it leads" form of editor. That editor will have to decide if that story is worth the lost revenue.
This should reduce the one-upsmanship among spree killers to get more press by trying to horrify us more than the last guy.