diff --git a/doc/emacs/programs.texi b/doc/emacs/programs.texi
index 01a1462044c..8ab5033795d 100644
--- a/doc/emacs/programs.texi
+++ b/doc/emacs/programs.texi
@@ -378,6 +378,10 @@ Imenu
 symbol @code{imenu--sort-by-name} as the value.  You can also
 define your own comparison function by writing Lisp code.
 
+  You can also customize how Imenu completions are sorted by changing
+the variable @code{completion-category-overrides} and setting its
+@code{display-sort-function} for the category @code{imenu}.
+
   If Eglot is activated for the current buffer's project
 (@pxref{Projects}) and the current buffer's major mode, Eglot provides
 its own facility for producing the buffer's index based on the
diff --git a/etc/NEWS b/etc/NEWS
index 8a2c8950fd8..19564062d9f 100644
--- a/etc/NEWS
+++ b/etc/NEWS
@@ -1046,6 +1046,11 @@ point is not in a comment or a string.  It is by default bound to
 It defines whether to flatten the list of sections in an imenu
 or show it nested.
 
++++
+*** Imenu completions now can be sorted.
+You can customize the option 'completion-category-overrides'
+and set 'display-sort-function' for the category 'imenu'.
+
 ** Which Function mode
 
 +++
diff --git a/lisp/imenu.el b/lisp/imenu.el
index 93a544ff550..f255dcc7148 100644
--- a/lisp/imenu.el
+++ b/lisp/imenu.el
@@ -115,7 +115,10 @@ imenu-after-jump-hook
 (defcustom imenu-sort-function nil
   "The function to use for sorting the index mouse-menu.
 
-Affects only the mouse index menu.
+Affects only the mouse index menu.  If you want to change
+the sorting order of completions, you can customize
+the option `completion-category-overrides' and set
+`display-sort-function' for the category `imenu'.
 
 Set this to nil if you don't want any sorting (faster).
 The items in the menu are then presented in the order they were found