diff --git a/src/client/composer/composer-widget.vala b/src/client/composer/composer-widget.vala
index 5b81edef..f91e8387 100644
--- a/src/client/composer/composer-widget.vala
+++ b/src/client/composer/composer-widget.vala
@@ -2010,23 +2010,9 @@ public class ComposerWidget : Gtk.EventBox {
                 return Gdk.EVENT_STOP;
         }
 
-        if ((event.state & Gdk.ModifierType.MOD1_MASK) != 0)
-            return Gdk.EVENT_PROPAGATE;
-        if ((event.state & Gdk.ModifierType.CONTROL_MASK) != 0) {
-            if (event.keyval == Gdk.Key.Tab) {
-                child_focus(Gtk.DirectionType.TAB_FORWARD);
-                return Gdk.EVENT_STOP;
-            }
-            if (event.keyval == Gdk.Key.ISO_Left_Tab) {
-                child_focus(Gtk.DirectionType.TAB_BACKWARD);
-                return Gdk.EVENT_STOP;
-            }
-            return Gdk.EVENT_PROPAGATE;
-        }
-
         if (this.can_delete_quote) {
             this.can_delete_quote = false;
-            if (event.keyval == Gdk.Key.BackSpace) {
+            if (event.is_modifier == 0 && event.keyval == Gdk.Key.BackSpace) {
                 this.editor.delete_quoted_message();
                 return Gdk.EVENT_STOP;
             }
diff --git a/ui/composer-web-view.js b/ui/composer-web-view.js
index 7ef4b936..026fc210 100644
--- a/ui/composer-web-view.js
+++ b/ui/composer-web-view.js
@@ -53,7 +53,13 @@ ComposerPageState.prototype = {
 
         this.messageBody = document.getElementById(ComposerPageState.BODY_ID);
         this.messageBody.addEventListener("keydown", function(e) {
-            if (e.keyCode == 9) {
+            // Should be using 'e.key == "Tab"' here, but that was
+            // only fixed in WK in Oct 2016 (WK Bug 36267). Migrate to
+            // that when we can rely on it being in WebKitGTK.
+            if (e.keyIdentifier == "U+0009"
+                && !e.ctrlKey
+                && !e.altKey
+                && !e.metaKey) {
                 if (!e.shiftKey) {
                     state.tabOut();
                 } else {