diff --git a/runtime/menu.vim b/runtime/menu.vim
index c9acf76ca8..edd628f4b4 100644
--- a/runtime/menu.vim
+++ b/runtime/menu.vim
@@ -2,7 +2,7 @@
 " You can also use this as a start for your own set of menus.
 "
 " Maintainer:	The Vim Project <https://github.com/vim/vim>
-" Last Change:	2023 Aug 10
+" Last Change:	2025 Aug 10
 " Former Maintainer:	Bram Moolenaar <Bram@vim.org>
 
 " Note that ":an" (short for ":anoremenu") is often used to make a menu work
@@ -797,8 +797,21 @@ def s:BMShow()
 enddef
 
 def s:BMHash(name: string): number
-  # Make name all upper case, so that chars are between 32 and 96
-  var nm = substitute(name, ".*", '\U\0', "")
+  # Create a sortable numeric hash of the name. This number has to be within
+  # the bounds of a signed 32-bit integer as this is what Vim GUI uses
+  # internally for the index.
+
+  # Make name all upper case, so that alphanumeric chars are between 32 and 96
+  var nm = toupper(name)
+
+  if char2nr(nm[0]) < 32 || char2nr(nm[0]) > 96
+    # We don't have an ASCII character, so just return the raw character value
+    # for first character (clamped to 2^31) and set the high bit to make it
+    # sort after other items. This means only the first character will be
+    # sorted, unfortunately.
+    return or(and(char2nr(nm), 0x7fffffff), 0x40000000)
+  endif
+
   var sp: number
   if has("ebcdic")
     # HACK: Replace all non alphabetics with 'Z'
@@ -808,12 +821,18 @@ def s:BMHash(name: string): number
   else
     sp = char2nr(' ')
   endif
-  # convert first six chars into a number for sorting:
-  return (char2nr(nm[0]) - sp) * 0x800000 + (char2nr(nm[1]) - sp) * 0x20000 + (char2nr(nm[2]) - sp) * 0x1000 + (char2nr(nm[3]) - sp) * 0x80 + (char2nr(nm[4]) - sp) * 0x20 + (char2nr(nm[5]) - sp)
+  # convert first five chars into a number for sorting by compressing each
+  # char into 5 bits (0-63), to a total of 30 bits. If any character is not
+  # ASCII, it will simply be clamped to prevent overflow.
+  return (max([0, min([63, char2nr(nm[0]) - sp])]) << 24) +
+    (max([0, min([63, char2nr(nm[1]) - sp])]) << 18) +
+    (max([0, min([63, char2nr(nm[2]) - sp])]) << 12) +
+    (max([0, min([63, char2nr(nm[3]) - sp])]) <<  6) +
+    max([0, min([63, char2nr(nm[4]) - sp])])
 enddef
 
 def s:BMHash2(name: string): string
-  var nm = substitute(name, ".", '\L\0', "")
+  var nm = tolower(name[0])
   if nm[0] < 'a' || nm[0] > 'z'
     return '&others.'
   elseif nm[0] <= 'd'
diff --git a/src/testdir/test_gui.vim b/src/testdir/test_gui.vim
index 16e8f9134d..b088492718 100644
--- a/src/testdir/test_gui.vim
+++ b/src/testdir/test_gui.vim
@@ -1767,4 +1767,37 @@ func Test_CursorHold_not_triggered_at_startup()
   call assert_equal(['g:cursorhold_triggered=0'], found)
 endfunc
 
+" Test that Buffers menu generates the correct index for different buffer
+" names for sorting.
+func Test_Buffers_Menu()
+  doautocmd LoadBufferMenu VimEnter
+
+  " Non-ASCII characters only use the first character as idx
+  let idx_emoji = or(char2nr('😑'), 0x40000000)
+
+  " Only first five letters are used for alphanumeric:
+  " ('a'-32) << 24 + ('b'-32) << 18 + ('c'-32) << 12 + ('d'-32) << 6 + ('e'-32)
+  let idx_abcde = 0x218A3925
+  " ('a'-32) << 24 + ('b'-32) << 18 + ('c'-32) << 12 + ('d'-32) << 6 + ('f'-32)
+  let idx_abcdf = 0x218A3926
+  " ('a'-32) << 24 + 63 (clamped) << 18 + ('c'-32) << 12 + ('d'-32) << 6 + ('e'-32)
+  let idx_a_emoji_cde = 0x21FE3925
+
+  let names = ['😑', '😑1', '😑2', 'abcde', 'abcdefghi', 'abcdf', 'a😑cde']
+  let indices = [idx_emoji, idx_emoji, idx_emoji, idx_abcde, idx_abcde, idx_abcdf, idx_a_emoji_cde]
+  for i in range(len(names))
+    let name = names[i]
+    let idx = indices[i]
+    exe ':badd ' .. name
+    let nr = bufnr('$')
+
+    let cmd = printf(':amenu Buffers.%s\ (%d)', name, nr)
+    let menu = split(execute(cmd), '\n')[1]
+    call assert_inrange(0, 0x7FFFFFFF, idx)
+    call assert_match('^' .. idx .. ' '.. name, menu)
+  endfor
+
+  %bw!
+endfunc
+
 " vim: shiftwidth=2 sts=2 expandtab
diff --git a/src/version.c b/src/version.c
index b28e3b2a4a..78cf50877d 100644
--- a/src/version.c
+++ b/src/version.c
@@ -719,6 +719,8 @@ static char *(features[]) =
 
 static int included_patches[] =
 {   /* Add new patch number below this line */
+/**/
+    1623,
 /**/
     1622,
 /**/