diff --git a/src/testdir/test_functions.vim b/src/testdir/test_functions.vim
index 17a87d8..715da0b 100644
--- a/src/testdir/test_functions.vim
+++ b/src/testdir/test_functions.vim
@@ -3217,6 +3217,31 @@
   call assert_equal(-1, screenattr(-1, -1))
   call assert_equal(-1, screenchar(-1, -1))
   call assert_equal([], screenchars(-1, -1))
+
+  " Run this in a separate Vim instance to avoid messing up.
+  let after =<< trim [CODE]
+    scriptencoding utf-8
+    call setline(1, '口')
+    redraw
+    call assert_equal(0, screenattr(1, 1))
+    call assert_equal(char2nr('口'), screenchar(1, 1))
+    call assert_equal([char2nr('口')], screenchars(1, 1))
+    call assert_equal('口', screenstring(1, 1))
+    call writefile(v:errors, 'Xresult')
+    qall!
+  [CODE]
+
+  let encodings = ['utf-8', 'cp932', 'cp936', 'cp949', 'cp950']
+  if !has('win32')
+    let encodings += ['euc-jp']
+  endif
+  for enc in encodings
+    let msg = 'enc=' .. enc
+    if RunVim([], after, $'--clean --cmd "set encoding={enc}"')
+      call assert_equal([], readfile('Xresult'), msg)
+    endif
+    call delete('Xresult')
+  endfor
 endfunc
 
 " Test for getcurpos() and setpos()
diff --git a/src/testdir/test_utf8.vim b/src/testdir/test_utf8.vim
index 610566f..3bb7459 100644
--- a/src/testdir/test_utf8.vim
+++ b/src/testdir/test_utf8.vim
@@ -135,6 +135,19 @@
   call assert_equal("B", screenstring(1, 2))
   call assert_equal("C\u0308", screenstring(1, 3))
 
+  " 1-cell, with 6 composing characters
+  set maxcombine=6
+  call setline(1, ["ABC" .. repeat("\u0308", 6)])
+  redraw
+  call assert_equal([0x0041], screenchars(1, 1))
+  call assert_equal([0x0042], 1->screenchars(2))
+  " This should not use uninitialized memory
+  call assert_equal([0x0043] + repeat([0x0308], 6), screenchars(1, 3))
+  call assert_equal("A", screenstring(1, 1))
+  call assert_equal("B", screenstring(1, 2))
+  call assert_equal("C" .. repeat("\u0308", 6), screenstring(1, 3))
+  set maxcombine&
+
   " 2-cells, with composing characters
   let text = "\u3042\u3044\u3046\u3099"
   call setline(1, text)