Edinburgh Airport said it has modified its proposals for changes to its flight paths following its latest public consultation.
Residents below the new routes said they were concerned about increased noise and the impact on communities.
The airport said it would only use any new routes when "they are required, and that we should explain very clearly when that is and why".
It said it had also restricted the routes to peak hours.
However, campaigners said the airport had only published "vague information" about the changed plans.
Edinburgh Airport submitted its revised Airspace Change proposal to the Civil Aviation Authority on Thursday.
Gordon Dewar, chief executive of Edinburgh Airport, said: "The listening exercise we embarked upon has been crucial to our thinking and we have altered our application following the feedback we received, demonstrating the importance of that public engagement.
"We are now favouring a phased approach based on the premise that we should only use any new routes when they are required, and that we should explain very clearly when that is and why.
"We've also restricted these routes to peak hours, substantially reducing any potential impact on communities whilst delivering the capacity when it is required.
"We believe this application will deliver future economic growth for Edinburgh and Scotland, and strikes the best possible balance between those benefits and our communities' requirements, our operational requirements and the requirements of our regulator, the CAA."
Edinburgh Airport said the changes were necessary to cope with increasing numbers of passengers.
There have been two public consultations held into the proposals.
The results of the first consultation were published in November.
It ended a week later than planned after the airport was forced to apologise for losing almost 200 responses.
Almost 4,000 people responded to a second public consultation proposal.
Campaign group Edinburgh Airport Watch said: "We call on the airport to halt this flawed process now.
"The CAA must scrutinise this application very carefully, and understand that there is no community support for these changes.
"With 52% of responders being 'negative', we do not accept that there is any evidence that these changes have any 'broad support' among communities as the airport claims.
"Noise complaints to Edinburgh Airport are at record levels, the daily misery being caused to people in their homes, schools and businesses by the airport and its Air Traffic Controllers, NATS, cannot be allowed to continue.
"We call on our government to intervene and ask serious questions about whose interests are being served by such radical proposals for change to flight paths that will have life-altering consequences for the health and wellbeing of hundreds of thousands of people across east central Scotland."