diff --git a/doc/lispref/display.texi b/doc/lispref/display.texi
index c2ebf81f669..13d0a1b458d 100644
--- a/doc/lispref/display.texi
+++ b/doc/lispref/display.texi
@@ -1863,10 +1863,10 @@ from the buffer.
 @kindex keymap @r{(overlay property)}
 If this property is non-@code{nil}, it specifies a keymap for a
 portion of the text.  This keymap takes precedence over most other
-keymaps (@pxref{Active Keymaps}), and it is used when the character
-after point is within the overlay, or would be when taking the front-
-and rear-advance properties into consideration (@pxref{Managing
-Overlays}).
+keymaps (@pxref{Active Keymaps}), and it is used when point is within
+the overlay, where the front-
+and rear-advance properties define whether the boundaries are
+considered as being @emph{within} or not.
 
 @item local-map
 @kindex local-map @r{(overlay property)}