Ceiling panels for use in a grid-type suspended ceiling (10) each comprise a thin flexible scrim (40) that is of insufficient rigidity to consistently maintain a substantially planar form when installed in the grid-type suspended ceiling. These embodiments also present a rigidizing and engagement member (60, 122, 161) that attaches to only a relatively minor portion of the thin flexible scrim and that is configured and arranged to substantially increase and maintain rigidity of the thin flexible scrim such that the thin flexible scrim will consistently maintain a substantially planar form when installed in the grid-type suspended ceiling and that will also serve to engage at least one grid runner of the grid-type suspended ceiling to thereby maintain the thin flexible scrim in an installed position within the grid-type suspended ceiling.