New traffic lights that go green for riders before other traffic would be installed at 14 sites, if approved after consultation.
They are already in use at the Leith Walk/McDonald Road junction.
It follows red cycle lanes for riders to cross tram lines more safely being brought in last autumn.
Advanced stop lines for cyclists at traffic lights at five junctions are also due to be completed by the end of the month.
The work was triggered by the death of Malaysian student Zhi Min Soh, whose bike wheels became caught in tram tracks last May at the junction of Shandwick Place and Queensferry Street.
The plans are part of a public consultation which was launched on the council's website today and runs until 11 April.
If approved, most are expected to be implemented towards the end of the year
They also include two options for the Haymarket junction at Grosvenor Street, changes to the alignment of the cycle lane at Haymarket Station, and a new mandatory cycle lane where Princes Street meets South St Andrew Street.The council also proposes a new traffic island at Haymarket Yards, a new cycle crossing over the tram route at Cultins Road in Edinburgh Park, and improvements to the traffic island and advanced stop line box at the junction of Princes Street and South Charlotte Street. Transport convener Lesley Macinnes said: "With the first phase of cycle safety improvements already in place - and, according to our feedback, well-received by cyclists - and the second phase just weeks away from being implemented, we're now looking to the public for feedback on our proposed designs for phase three, which we aim to put in place later this year. "Road safety is absolutely paramount and we've been working extremely closely with our partners to refine these designs.
"Early release signals for cyclists have been credited with reducing collisions in cities where they're already used so these are a particularly desirable option.
The council said a fourth and final phase would involve changes to the road layout at the Princes Street/Lothian Road/Shandwick Place/Queensferry Street/Hope Street junction to improve safety for cyclists and pedestrians.
Ian Maxwell, of Spokes, the Lothian cycle campaign, said: "Signalled advanced stop lines have been used successfully for decades in other countries to give cyclists a better chance to cross junctions ahead of other traffic.
"This reduces the risk of getting cut off by turning vehicles and also avoids some of the racing starts when the lights go green.
"It is encouraging to see Edinburgh making use of such ideas, and we hope to see other 'radical' options such as traffic restraint to make central Edinburgh better for pedestrians, cyclists and public transport users."
A spokeswoman for cycle path developers Sustrans Scotland said: “Cycling safety is of utmost importance to us and we welcome any initiative which helps to ensure people feel safe when travelling by bike around Edinburgh.
“Early release signals have been used very successfully across the continent and have helped to reduce the number of collisions.
"The signals will help improve safety and enable a better flow of people on bikes as they travel across the capital.”