Using numpy to efficiently convert 16-bit image data to 8 bit for display, with intensity scaling

I frequently convert 16-bit grayscale image data to 8-bit image data for display. It's almost always useful to adjust the minimum and maximum display intensity to highlight the 'interesting' parts of the image.

The code below does roughly what I want, but it's ugly and inefficient, and makes many intermediate copies of the image data. How can I achieve the same result with a minimum memory footprint and processing time?

import numpy

image_data = numpy.random.randint( #Realistic images would be much larger
    low=100, high=14000, size=(1, 5, 5)).astype(numpy.uint16)

display_min = 1000
display_max = 10000.0

print(image_data)
threshold_image = ((image_data.astype(float) - display_min) *
                   (image_data > display_min))
print(threshold_image)
scaled_image = (threshold_image * (255. / (display_max - display_min)))
scaled_image[scaled_image > 255] = 255
print(scaled_image)
display_this_image = scaled_image.astype(numpy.uint8)
print(display_this_image)