diff --git a/xwords4/android/XWords4/res/menu/games_list_menu.xml b/xwords4/android/XWords4/res/menu/games_list_menu.xml
index 424e718ab..04605844e 100644
--- a/xwords4/android/XWords4/res/menu/games_list_menu.xml
+++ b/xwords4/android/XWords4/res/menu/games_list_menu.xml
@@ -69,18 +69,22 @@
           />
 
     <!-- Group items -->
+    <item android:id="@+id/list_group_moveup"
+          android:title="@string/list_group_moveup"
+          android:showAsAction="ifRoom"
+          android:icon="@drawable/up__gen"
+          />
+    <item android:id="@+id/list_group_movedown"
+          android:title="@string/list_group_movedown"
+          android:showAsAction="ifRoom"
+          android:icon="@drawable/down__gen"
+          />
     <item android:id="@+id/list_group_default"
           android:title="@string/list_group_default"
           />
     <item android:id="@+id/list_group_rename"
           android:title="@string/list_group_rename"
           />
-    <item android:id="@+id/list_group_moveup"
-          android:title="@string/list_group_moveup"
-          />
-    <item android:id="@+id/list_group_movedown"
-          android:title="@string/list_group_movedown"
-          />
 
     <!-- Debug only menuitems -->
     <item android:id="@+id/gamel_menu_checkupdates"
diff --git a/xwords4/android/XWords4/src/org/eehouse/android/xw4/GamesList.java b/xwords4/android/XWords4/src/org/eehouse/android/xw4/GamesList.java
index 9af63e912..142234569 100644
--- a/xwords4/android/XWords4/src/org/eehouse/android/xw4/GamesList.java
+++ b/xwords4/android/XWords4/src/org/eehouse/android/xw4/GamesList.java
@@ -113,8 +113,6 @@ public class GamesList extends XWExpandableListActivity
 
     private static final int[] ONEGROUP_ITEMS = {
         R.id.list_group_rename,
-        R.id.list_group_moveup,
-        R.id.list_group_movedown,
     };
 
     private static boolean s_firstShown = false;
@@ -643,16 +641,27 @@ public class GamesList extends XWExpandableListActivity
             Utils.setItemVisible( menu, id, 1 == nGroupsSelected );
         }
 
+        int selGroupPos = -1;
+        if ( 1 == nGroupsSelected ) {
+            selGroupPos = m_selectedGroups.iterator().next();
+        }
+
         // You can't delete the default group, nor make it the default
         boolean defaultAvail = 1 == nGroupsSelected;
         if ( defaultAvail ) {
-            int selPos = m_selectedGroups.iterator().next();
-            long selID = m_adapter.getGroupIDFor( selPos );
+            long selID = m_adapter.getGroupIDFor( selGroupPos );
             defaultAvail = selID != XWPrefs.getDefaultNewGameGroup( this );
         }
         Utils.setItemVisible( menu, R.id.list_group_default, defaultAvail );
         Utils.setItemVisible( menu, R.id.list_group_delete, defaultAvail );
 
+        // Move up/down enabled for groups if not the top-most or bottommost
+        // selected
+        boolean enable = 0 < selGroupPos;
+        Utils.setItemVisible( menu, R.id.list_group_moveup, enable );
+        enable = 0 <= selGroupPos && selGroupPos + 1 < m_adapter.getGroupCount();
+        Utils.setItemVisible( menu, R.id.list_group_movedown, enable );
+
         // New game available when nothing selected or one group
         Utils.setItemVisible( menu, R.id.gamel_menu_newgame,
                               nothingSelected || 1 == nGroupsSelected );