How to remove shiny patches?

[Susan Kuban]

I have applied some dark greens in thick paint that have dried much shinier than the areas around them. I like the texture that exists in these patches, but the shine looks bad against the flat background. I know I could try to oil out the flatter areas, but really the entire painting is fairly flat. It's the shiny spots that are the negatives, not the flat areas. Can anyone suggest how to remove the shine?

Thanks, Susan