diff --git a/src/nvim/insexpand.c b/src/nvim/insexpand.c
index 05bd31061c..0714269a67 100644
--- a/src/nvim/insexpand.c
+++ b/src/nvim/insexpand.c
@@ -2929,11 +2929,18 @@ static void copy_global_to_buflocal_cb(Callback *globcb, Callback *bufcb)
 const char *did_set_completefunc(optset_T *args)
 {
   buf_T *buf = (buf_T *)args->os_buf;
-  if (option_set_callback_func(buf->b_p_cfu, &cfu_cb) == FAIL) {
-    return e_invarg;
+  int retval;
+
+  if (args->os_flags & OPT_LOCAL) {
+    retval = option_set_callback_func(args->os_newval.string.data, &buf->b_cfu_cb);
+  } else {
+    retval = option_set_callback_func(args->os_newval.string.data, &cfu_cb);
+    if (retval == OK && !(args->os_flags & OPT_GLOBAL)) {
+      set_buflocal_cfu_callback(buf);
+    }
   }
-  set_buflocal_cfu_callback(buf);
-  return NULL;
+
+  return retval == FAIL ? e_invarg : NULL;
 }
 
 /// Copy the global 'completefunc' callback function to the buffer-local
@@ -2950,11 +2957,18 @@ void set_buflocal_cfu_callback(buf_T *buf)
 const char *did_set_omnifunc(optset_T *args)
 {
   buf_T *buf = (buf_T *)args->os_buf;
-  if (option_set_callback_func(buf->b_p_ofu, &ofu_cb) == FAIL) {
-    return e_invarg;
+  int retval;
+
+  if (args->os_flags & OPT_LOCAL) {
+    retval = option_set_callback_func(args->os_newval.string.data, &buf->b_ofu_cb);
+  } else {
+    retval = option_set_callback_func(args->os_newval.string.data, &ofu_cb);
+    if (retval == OK && !(args->os_flags & OPT_GLOBAL)) {
+      set_buflocal_ofu_callback(buf);
+    }
   }
-  set_buflocal_ofu_callback(buf);
-  return NULL;
+
+  return retval == FAIL ? e_invarg : NULL;
 }
 
 /// Copy the global 'omnifunc' callback function to the buffer-local 'omnifunc'
diff --git a/src/nvim/tag.c b/src/nvim/tag.c
index e3a6f87335..d07ba9c475 100644
--- a/src/nvim/tag.c
+++ b/src/nvim/tag.c
@@ -228,20 +228,18 @@ static Callback tfu_cb;          // 'tagfunc' callback function
 const char *did_set_tagfunc(optset_T *args)
 {
   buf_T *buf = (buf_T *)args->os_buf;
+  int retval;
 
-  callback_free(&tfu_cb);
-  callback_free(&buf->b_tfu_cb);
-
-  if (*buf->b_p_tfu == NUL) {
-    return NULL;
+  if (args->os_flags & OPT_LOCAL) {
+    retval = option_set_callback_func(args->os_newval.string.data, &buf->b_tfu_cb);
+  } else {
+    retval = option_set_callback_func(args->os_newval.string.data, &tfu_cb);
+    if (retval == OK && !(args->os_flags & OPT_GLOBAL)) {
+      set_buflocal_tfu_callback(buf);
+    }
   }
 
-  if (option_set_callback_func(buf->b_p_tfu, &tfu_cb) == FAIL) {
-    return e_invarg;
-  }
-
-  callback_copy(&buf->b_tfu_cb, &tfu_cb);
-  return NULL;
+  return retval == FAIL ? e_invarg : NULL;
 }
 
 #if defined(EXITFREE)
diff --git a/test/old/testdir/test_ins_complete.vim b/test/old/testdir/test_ins_complete.vim
index c6f64840a5..250559cc4a 100644
--- a/test/old/testdir/test_ins_complete.vim
+++ b/test/old/testdir/test_ins_complete.vim
@@ -2535,6 +2535,35 @@ func Test_completefunc_callback()
     call feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
     call assert_equal([[1, ''], [0, 'five']], g:CompleteFunc2Args)
     bw!
+
+    #" :setlocal and :setglobal
+    set completefunc&
+    setlocal completefunc=function('g:CompleteFunc1',\ [22])
+    call setline(1, 'sun')
+    LET g:CompleteFunc1Args = []
+    call feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
+    call assert_equal([[22, 1, ''], [22, 0, 'sun']], g:CompleteFunc1Args)
+    new
+    call setline(1, 'sun')
+    LET g:CompleteFunc1Args = []
+    call assert_fails('call feedkeys("A\<C-X>\<C-U>\<Esc>", "x")', 'E764:')
+    call assert_equal([], g:CompleteFunc1Args)
+    bw!
+    setglobal completefunc=function('g:CompleteFunc1',\ [23])
+    call setline(1, 'sun')
+    call feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
+    call assert_equal([[22, 1, ''], [22, 0, 'sun']], g:CompleteFunc1Args)
+    new
+    call setline(1, 'sun')
+    LET g:CompleteFunc1Args = []
+    call feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
+    call assert_equal([[23, 1, ''], [23, 0, 'sun']], g:CompleteFunc1Args)
+    setlocal completefunc&
+    call setline(1, 'sun')
+    LET g:CompleteFunc1Args = []
+    call assert_fails('call feedkeys("A\<C-X>\<C-U>\<Esc>", "x")', 'E764:')
+    call assert_equal([], g:CompleteFunc1Args)
+    :%bw!
   END
   call CheckLegacyAndVim9Success(lines)
 
@@ -2809,6 +2838,35 @@ func Test_omnifunc_callback()
     call feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
     call assert_equal([[1, ''], [0, 'nine']], g:OmniFunc2Args)
     bw!
+
+    #" :setlocal and :setglobal
+    set omnifunc&
+    setlocal omnifunc=function('g:OmniFunc1',\ [22])
+    call setline(1, 'sun')
+    LET g:OmniFunc1Args = []
+    call feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
+    call assert_equal([[22, 1, ''], [22, 0, 'sun']], g:OmniFunc1Args)
+    new
+    call setline(1, 'sun')
+    LET g:OmniFunc1Args = []
+    call assert_fails('call feedkeys("A\<C-X>\<C-O>\<Esc>", "x")', 'E764:')
+    call assert_equal([], g:OmniFunc1Args)
+    bw!
+    setglobal omnifunc=function('g:OmniFunc1',\ [23])
+    call setline(1, 'sun')
+    call feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
+    call assert_equal([[22, 1, ''], [22, 0, 'sun']], g:OmniFunc1Args)
+    new
+    call setline(1, 'sun')
+    LET g:OmniFunc1Args = []
+    call feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
+    call assert_equal([[23, 1, ''], [23, 0, 'sun']], g:OmniFunc1Args)
+    setlocal omnifunc&
+    call setline(1, 'sun')
+    LET g:OmniFunc1Args = []
+    call assert_fails('call feedkeys("A\<C-X>\<C-O>\<Esc>", "x")', 'E764:')
+    call assert_equal([], g:OmniFunc1Args)
+    :%bw!
   END
   call CheckLegacyAndVim9Success(lines)
 
diff --git a/test/old/testdir/test_tagfunc.vim b/test/old/testdir/test_tagfunc.vim
index 19fc8de8dd..052b685a18 100644
--- a/test/old/testdir/test_tagfunc.vim
+++ b/test/old/testdir/test_tagfunc.vim
@@ -257,13 +257,37 @@ func Test_tagfunc_callback()
     call assert_fails("set tagfunc=funcref('abc')", "E700:")
 
     #" set 'tagfunc' to a non-existing function
-    LET &tagfunc = function('g:TagFunc2', [21])
+    LET &tagfunc = function('g:TagFunc2')
     LET g:TagFunc2Args = []
     call assert_fails("set tagfunc=function('NonExistingFunc')", 'E700:')
     call assert_fails("LET &tagfunc = function('NonExistingFunc')", 'E700:')
-    call assert_fails("tag axb123", 'E426:')
-    call assert_equal([], g:TagFunc2Args)
+    call assert_fails("tag axb123", 'E433:')
+    call assert_equal(['axb123', '', {}], g:TagFunc2Args)
     bw!
+
+    #" :setlocal and :setglobal
+    set tagfunc&
+    setlocal tagfunc=function('g:TagFunc1',\ [22])
+    LET g:TagFunc1Args = []
+    call assert_fails("tag a22", 'E433:')
+    call assert_equal([22, 'a22', '', {}], g:TagFunc1Args)
+    new
+    LET g:TagFunc1Args = []
+    call assert_fails("tag a22", 'E433:')
+    call assert_equal([], g:TagFunc1Args)
+    bw!
+    setglobal tagfunc=function('g:TagFunc1',\ [23])
+    call assert_fails("tag a22", 'E433:')
+    call assert_equal([22, 'a22', '', {}], g:TagFunc1Args)
+    new
+    LET g:TagFunc1Args = []
+    call assert_fails("tag a23", 'E433:')
+    call assert_equal([23, 'a23', '', {}], g:TagFunc1Args)
+    setlocal tagfunc&
+    LET g:TagFunc1Args = []
+    call assert_fails("tag a23", 'E433:')
+    call assert_equal([], g:TagFunc1Args)
+    :%bw!
   END
   call CheckLegacyAndVim9Success(lines)