Union officials and bosses at Westcountry Ambulance Service have entered a "cooling off" period.
It follows an overwhelming vote by staff earlier this month to reject proposals to alter the way some calls are dealt with at night.
Unison members had been asked to vote for a ballot on whether to take industrial action.
Having failed to agree, union officials and ambulance bosses are expected to meet again later this week.
Plans to change emergency cover were confirmed in January by Westcountry Ambulance Trust, which says the changes will mean greater flexibility and more resources.
The trust wants to put more emphasis on rapid response vehicles (RRVs) and emergency care assistants working on their own.
But union officials argue that patient safety could be compromised by scaling down 24-hour cover and the use of RRVs will reduce cover in some rural areas.
Despite the result of the ballot, Unison says a vote for strike action is very unlikely, although it could not rule out some other form of industrial action.