I believe if we use only an outer scrollbar, this means we need to render the entire list of printers, since the iron-list for the print destinations would need to always be full height of all the printers. This removes the benefit of using iron list and will cause the UI to be very slow for users with large numbers of printers, because we will need to render thousands of printers even though they are not actually visible on the screen.

I am working on improving the sizing of these lists so that the outer scrollbar will not show up unless the dialog is very short. That would allow us to keep the UI responsive for large numbers of printers and would mean there would only be 1 scrollbar in the majority of cases; would that be acceptable as an alternative solution?

Yup! That would work great as well. Thanks Rebekah

 Issue 885118  has been merged into this issue.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/fa2e08937a5c741634ebb903330a5e46986a4532

commit fa2e08937a5c741634ebb903330a5e46986a4532
Author: rbpotter <rbpotter@chromium.org>
Date: Fri Sep 21 17:54:21 2018

Print Preview Refresh: Fix iron-list sizing

Fix the sizing of the print destinations list so that it is always set
to the maximum of the available space and 3 destinations of height.

This will ensure there is no double scrollbar unless the dialog is
extremely short.

Bug:  884741 
Change-Id: Ieba1a4e634d667b2e6e5567cf6f80f5962bd0fde
Reviewed-on: https://chromium-review.googlesource.com/1235120
Reviewed-by: Scott Chen <scottchen@chromium.org>
Commit-Queue: Rebekah Potter <rbpotter@chromium.org>
Cr-Commit-Position: refs/heads/master@{#593250}
[modify] https://crrev.com/fa2e08937a5c741634ebb903330a5e46986a4532/chrome/browser/resources/print_preview/new/destination_dialog.html
[modify] https://crrev.com/fa2e08937a5c741634ebb903330a5e46986a4532/chrome/browser/resources/print_preview/new/destination_dialog.js
[modify] https://crrev.com/fa2e08937a5c741634ebb903330a5e46986a4532/chrome/browser/resources/print_preview/new/destination_list.html
[modify] https://crrev.com/fa2e08937a5c741634ebb903330a5e46986a4532/chrome/browser/resources/print_preview/new/destination_list.js
[modify] https://crrev.com/fa2e08937a5c741634ebb903330a5e46986a4532/chrome/browser/resources/print_preview/new/print_preview_shared_css.html

Should now be fixed, please verify and re-open if not.

Verified