Some minor crimes will no longer be investigated by police, as part of a project being piloted in the North-east.
Police Scotland said it wants to give officers more time to focus on responding to emergencies and keeping people safe from harm.
An example of where no further action may be taken was a garden theft with no CCTV or eye-witness evidence.
Police Scotland said: "Hard choices are being made to deliver effective policing within the funding available."
The new pilot has been described as a "proportionate response to crime".
But it comes days after UK Home Secretary Suella Braverman said the police in England and Wales must investigate every theft and follow all reasonable leads to catch offenders.
Free to break law
Ms Braverman said it was "completely unacceptable" that criminals are often "effectively free to break certain laws".
Police Scotland said that, currently, members of the public may have to wait some time to hear whether their report of a crime is being investigated.
However, under the new approach the aim is to inform people of the decision more quickly.
Divisional commander Chief Supt Graeme Mackie told the BBC: "The pilot process will enable local police officers to focus on those crimes that have proportionate lines of inquiry and potentially enable them to give more time to local concerns and priorities in the area.
"We also know that, sometimes, people simply want to report a crime and we want to provide that service efficiently."
He added: "Please continue to report crime in your area.
Inquiry
"Local officers will continue to review closed reports to enable them to map local crime trends and this may mean an inquiry is reopened and investigated."
Scottish Conservative justice spokesman Russell Findlay MSP said the pilot was a result of "depleted policing" across Scotland.
"Police Scotland should be applauded for being so candid about the reality of their predicament, but communities deserve better than the SNP's weak approach to justice," he said.
"Ministers must be upfront with the public about whether this policy will potentially be rolled out elsewhere in Scotland."
Scottish Liberal Democrat justice spokesperson Liam McArthur MSP said: "The police are being forced to make terrible choices because the Scottish Government have expected them to do so much with so little for so long.
'Botched centralisation'
"The SNP's botched centralisation of policing and brutal cuts have hit officer and staff numbers hard."
The Scottish Government said in a statement: "While these decisions are a matter for the Chief Constable, it is vital Police Scotland continues to inspire public trust and maintains relationships with local communities.
"This will be crucial when the results of this pilot are examined to ensure local priorities continue to be met with no detriment to communities."