Index: trunk/src/org/openstreetmap/josm/gui/dialogs/LatLonDialog.java
===================================================================
--- trunk/src/org/openstreetmap/josm/gui/dialogs/LatLonDialog.java	(revision 8908)
+++ trunk/src/org/openstreetmap/josm/gui/dialogs/LatLonDialog.java	(revision 8909)
@@ -280,6 +280,12 @@
     @Override
     public void setVisible(boolean visible) {
+        final String preferenceKey = getClass().getName() + ".geometry";
         if (visible) {
-            WindowGeometry.centerInWindow(Main.parent, getSize()).applySafe(this);
+            new WindowGeometry(
+                    preferenceKey,
+                    WindowGeometry.centerInWindow(getParent(), getSize())
+            ).applySafe(this);
+        } else {
+            new WindowGeometry(this).remember(preferenceKey);
         }
         super.setVisible(visible);