diff --git a/runtime/menu.vim b/runtime/menu.vim
index 662eea9403..768bd0b769 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
@@ -790,8 +790,21 @@ func s:BMShow(...)
 endfunc
 
 func s:BMHash(name)
-  " Make name all upper case, so that chars are between 32 and 96
-  let nm = substitute(a: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
+  let nm = toupper(a:name)
+
+  if char2nr(nm->slice(0, 1)) < 32 || char2nr(nm->slice(0, 1)) > 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
+
   if has("ebcdic")
     " HACK: Replace all non alphabetics with 'Z'
     "       Just to make it work for now.
@@ -800,13 +813,19 @@ func s:BMHash(name)
   else
     let 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.
+  " Nvim: no << operator
+  return (max([0, min([63, char2nr(nm->slice(0, 1)) - sp])]) * 0x1000000) +
+        \ (max([0, min([63, char2nr(nm->slice(1, 2)) - sp])]) * 0x40000) +
+        \ (max([0, min([63, char2nr(nm->slice(2, 3)) - sp])]) * 0x1000) +
+        \ (max([0, min([63, char2nr(nm->slice(3, 4)) - sp])]) * 0x40) +
+        \ max([0, min([63, char2nr(nm->slice(4, 5)) - sp])])
 endfunc
 
 func s:BMHash2(name)
-  let nm = substitute(a:name, ".", '\L\0', "")
-  " Not exactly right for EBCDIC...
+  let nm = tolower(a:name->slice(0, 1))
   if nm[0] < 'a' || nm[0] > 'z'
     return '&others.'
   elseif nm[0] <= 'd'
diff --git a/test/old/testdir/test_gui.vim b/test/old/testdir/test_gui.vim
index 9780d22e4f..f2136f58ac 100644
--- a/test/old/testdir/test_gui.vim
+++ b/test/old/testdir/test_gui.vim
@@ -44,4 +44,37 @@ func Test_colorscheme()
   redraw!
 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