The Department for Transport has outlined the key specifications it expects the three groups bidding to run the London-Scotland line to meet.
Among the demands are a requirement to cut average journey times between London King's Cross and Edinburgh Waverley by May 2020, although the DfT does not say what it expects the minimum journey time to be.
At present, the average time from Edinburgh to London on the East Coast route is four hours and 23 minutes, although a new fleet of Hitachi trains which are due to replace the current rolling stock in 2019 are expected to reduce the average journey time to around four hours and five minutes.
The bidders include Inter City Railways Limited - a joint bid by Stagecoach and Virgin - and First Group. The third bidder is a joint bid by France-based Keolis, which already operates a number of rail and tram franchises south of the Border, and Eurostar International Ltd, which runs the cross-Channel franchise.
Rail Minister Stephen Hammond said: "Franchising has been a force for good for our railways, delivering record growth to an industry that was once in decline.
"The time is now right for us to find a long-term partner for the East Coast franchise, who can use their private sector expertise and knowledge to build on the significant investment planned for the route.
"I want to see innovative bids that provide value for money for taxpayers and deliver improved services for passengers and local businesses."
A condition of the contract that the successful bidder will guarantee to continue operating services to all current destinations, including Edinburgh, Aberdeen and Inverness.
The winning bidder will be announced in November with the new eight-year franchise due to begin next March. Bidders will also be expected to meet a target of running six trains an hour to and from London King's Cross during off-peak periods Monday to Friday.
However, campaigners have warned against returning the franchise the private sector, pointing out that it generated £208 million for the Treasury in 2012/13. The franchise has been under public ownership since July 2009.