A police authority has added another option to merger proposals agreed in October with neighbouring forces.
Smaller forces face being merged into larger ones
Because of the geographical proximity of the two forces Bedfordshire wants to explore the possibility of merging with Thames Valley Police.
The force has already agreed to look at an East Anglian force including Cambs, Essex, Herts, Norfolk and Suffolk.
Other options include a southern force with Herts and Essex and a western unit with Herts and Cambs.
Consultations on the four options will now be carried out with local MPs , community groups, parish and district councils plus other interested parties.
More efficiency needed
Police authority chairman Peter Conniff said: "We have put forward the best options as we see them, within the guidelines stipulated by the home secretary.
"Whilst we, alongside many other police authorities, would have been happy to retain our local primacy, the home secretary's instructions made it perfectly clear that to stay as we are now was not acceptable."
The need to consider amalgamation has come from a report by the Inspector of Constabulary Denis O'Connor, the former chief constable in Surrey.
His view is that forces of more than 4,000 officers were most efficient and his report called for mergers of smaller constabularies.
A preferred option must be submitted to the Home Office by 23 December.
Mr Conniff said: "My primary concern remains the provision of an improved policing service for people who live and work in Bedfordshire and Luton. Exactly how this is achieved remains to be seen.
"I should also stress that large-scale job losses are not envisaged as the home secretary has said that this exercise is about efficiency not cost-saving."