diff --git a/src/edit.c b/src/edit.c
index 672028b..e9a994f 100644
--- a/src/edit.c
+++ b/src/edit.c
@@ -2023,7 +2023,7 @@
      * Only use mod_mask for special keys, to avoid things like <S-Space>,
      * unless 'allow_modmask' is TRUE.
      */
-#ifdef MACOS_X
+#if defined(MACOS_X) || defined(FEAT_GUI_GTK)
     // Command-key never produces a normal key
     if (mod_mask & MOD_MASK_CMD)
 	allow_modmask = TRUE;
diff --git a/src/gui_gtk_x11.c b/src/gui_gtk_x11.c
index 87838b9..4dfa5ff 100644
--- a/src/gui_gtk_x11.c
+++ b/src/gui_gtk_x11.c
@@ -1119,11 +1119,14 @@
     if (state & GDK_MOD1_MASK)
 	modifiers |= MOD_MASK_ALT;
 #if GTK_CHECK_VERSION(2,10,0)
+    if (state & GDK_META_MASK)
+	modifiers |= MOD_MASK_META;
     if (state & GDK_SUPER_MASK)
-	modifiers |= MOD_MASK_META;
-#endif
+	modifiers |= MOD_MASK_CMD;
+#else
     if (state & GDK_MOD4_MASK)
-	modifiers |= MOD_MASK_META;
+	modifiers |= MOD_MASK_CMD;
+#endif
 
     return modifiers;
 }
diff --git a/src/gui_xim.c b/src/gui_xim.c
index c9b1c6c..c124e8b 100644
--- a/src/gui_xim.c
+++ b/src/gui_xim.c
@@ -1063,6 +1063,9 @@
     int
 xim_queue_key_press_event(GdkEventKey *event, int down)
 {
+#ifdef FEAT_GUI_GTK
+    if (event->state & GDK_SUPER_MASK) return FALSE;
+#endif
     if (down)
     {
 	// Workaround GTK2 XIM 'feature' that always converts keypad keys to
diff --git a/src/keymap.h b/src/keymap.h
index 6fddc7f..29e2a05 100644
--- a/src/keymap.h
+++ b/src/keymap.h
@@ -500,8 +500,8 @@
 #define MOD_MASK_2CLICK	    0x20	// use MOD_MASK_MULTI_CLICK
 #define MOD_MASK_3CLICK	    0x40	// use MOD_MASK_MULTI_CLICK
 #define MOD_MASK_4CLICK	    0x60	// use MOD_MASK_MULTI_CLICK
-#ifdef MACOS_X
-# define MOD_MASK_CMD	    0x80
+#if defined(MACOS_X) || defined(FEAT_GUI_GTK)
+# define MOD_MASK_CMD	    0x80        // aka SUPER
 #endif
 
 #define MOD_MASK_MULTI_CLICK	(MOD_MASK_2CLICK|MOD_MASK_3CLICK|MOD_MASK_4CLICK)
diff --git a/src/misc2.c b/src/misc2.c
index 169eb51..57ee287 100644
--- a/src/misc2.c
+++ b/src/misc2.c
@@ -817,7 +817,7 @@
     {MOD_MASK_MULTI_CLICK,	MOD_MASK_2CLICK,	(char_u)'2'},
     {MOD_MASK_MULTI_CLICK,	MOD_MASK_3CLICK,	(char_u)'3'},
     {MOD_MASK_MULTI_CLICK,	MOD_MASK_4CLICK,	(char_u)'4'},
-#ifdef MACOS_X
+#if defined(MACOS_X) || defined(FEAT_GUI_GTK)
     {MOD_MASK_CMD,		MOD_MASK_CMD,		(char_u)'D'},
 #endif
     // 'A' must be the last one
@@ -1130,7 +1130,11 @@
     int	    key0;
     int	    key1;
 
-    if (!(*modifiers & (MOD_MASK_SHIFT | MOD_MASK_CTRL | MOD_MASK_ALT)))
+    if (!(*modifiers & (MOD_MASK_SHIFT | MOD_MASK_CTRL | MOD_MASK_ALT
+#ifdef FEAT_GUI_GTK
+	    | MOD_MASK_CMD
+#endif
+    )))
 	return key;
 
     // TAB is a special case
@@ -1582,6 +1586,9 @@
 {
     if ((modifiers == MOD_MASK_SHIFT
 		|| modifiers == (MOD_MASK_SHIFT | MOD_MASK_ALT)
+#ifdef FEAT_GUI_GTK
+		|| modifiers == (MOD_MASK_SHIFT | MOD_MASK_CMD)
+#endif
 		|| modifiers == (MOD_MASK_SHIFT | MOD_MASK_META))
 	    && ((key >= '!' && key <= '/')
 		|| (key >= ':' && key <= 'Z')
diff --git a/src/testdir/test_mapping.vim b/src/testdir/test_mapping.vim
index e81173d..e361f3e 100644
--- a/src/testdir/test_mapping.vim
+++ b/src/testdir/test_mapping.vim
@@ -247,6 +247,24 @@
   iunmap <M-á>
 endfunc
 
+func Test_map_super_quotes()
+  if has('gui_gtk') || has('gui_gtk3') || has("macos")
+    imap <D-"> foo
+    call feedkeys("Go-\<*D-\">-\<Esc>", "xt")
+    call assert_equal("-foo-", getline('$'))
+    set nomodified
+    iunmap <D-">
+  endif
+endfunc
+
+func Test_map_super_multibyte()
+  if has('gui_gtk') || has('gui_gtk3') || has("macos")
+    imap <D-á> foo
+    call assert_match('i  <D-á>\s*foo', execute('imap'))
+    iunmap <D-á>
+  endif
+endfunc
+
 func Test_abbr_after_line_join()
   new
   abbr foo bar
diff --git a/src/version.c b/src/version.c
index 8f13f3f..10a70e3 100644
--- a/src/version.c
+++ b/src/version.c
@@ -705,6 +705,8 @@
 static int included_patches[] =
 {   /* Add new patch number below this line */
 /**/
+    58,
+/**/
     57,
 /**/
     56,