Thanks to all of you for your helpful suggestions. You've helped me to see some items more clearly (weak pun intended, sorry).

NOTE THE BLUE ARROW IN THE ATTACHED IMAGE. I had split the glasses body into its separate components. Then, I changed the "glasses" material to glass, turned off "cast shadows", and turned the reflectivity all the way down. This yielded the bad results that you saw in my first post.

Here's what I did to fix the problem:

NOTE THE RED ARROW IN THE ATTACHED IMAGE. I looked at the screen, and decided to edit the material from the "Body", and not from the sub-category of "glasses".

This did the trick. I discovered that it did no good to edit the material for the "glasses" as a separate item. I had to edit the material for the entire body.

Please note that the "material" assigned to the Body was nothing but a dull, flat white.

Something To Do At 3:00AM