I bought a lamp shade that I 'guessed' would fit, which was 15" diameter and 11" tall. After seeing it on my brass lamp, it was too 'short' so I took it back to the store to see if they had a larger size, preferably 2"-3" taller. There was no larger size, and I since was really fond of this shade, I decided to buy a smaller "harp" for $1.50 and try it. Bingo! It dropped the shade down a few inches, so it is a keeper. I may even try a shorter harp. Problem solved. I have never considered a smaller harp as an option to adjust shade height and coverage.
Here is a diagram of lamp parts:
Hope this tip helps you with shade dilemmas!