The coalition could look again at its proposals to introduce elected police commissioners.
Deputy prime minister Nick Clegg said ministers had not yet discussed proposals to slow down the implementation of the change by introducing a pilot scheme.
The suggestion has been made by Lib Dem peer Sally Hamwee, as the police reform and social responsibility bill works its way through the upper House.
"It's always best to work with the grain of the evidence and if you can pilot something in an initial period, people would think that's an entirely rational way of going about things," Mr Clegg told the Today programme.
"Of course we're prepared to look at it."
He said the basic proposal to introduce elected police commissioners, who would be tasked with controlling police force budgets and strategy, was "enshrined" in the coalition agreement, which ministers "treat like a tablet of stone".
"Whether you pilot it along the way is something which is a perfectly legitimate area of debate and it's a debate we're having at the moment," Mr Clegg added.
A recent poll by YouGov for Liberty showed that just 15% of the public trusted elected police and crime commissioners more than the present system to protect their family.
Sixty-five per cent preferred a chief constable reporting to a police authority, as is currently the case.