SSE had previously proposed to site 17 turbines at Brown's Holt and up to 22 turbines at Woolfox, but RES said that its revised proposals would be more modest in scale.
RES head of development in England David Cox said: "Both projects have great potential, offering excellent wind speeds and access. We will be reviewing the existing data about each site in some detail and expect to begin the process of drawing up our own plans for wind farms at these locations in the next few months."
The company said it expects to submit revised planning applications for the sites before the end of 2014.