JACS,
Many times I have sharp backgrounds with my Tamron 150-600mm telephoto lens. I achieve that by reducing the focal length, stopping down the lens, focusing in between the subject and the background (when there is a particular subject) and choosing my background. Sometimes I like a blurred background like when I showed my Red-winged Blackbird last week. Because the background was so far away, it turned out nice.
What telephoto lenses do you use? My other telephoto lenses are a Canon 55-250mm lens and a Canon 55-200mm lens. When I use those lenses if I use 55mm focal length and F9, almost all of my images are sharp at all distances from near to far away.