diff --git a/src/core/place.c b/src/core/place.c
index feb5c4cbf..01b0bd34d 100644
--- a/src/core/place.c
+++ b/src/core/place.c
@@ -353,7 +353,9 @@ find_most_freespace (MetaWindow *window,
 }
 
 static gboolean
-window_overlaps_focus_window (MetaWindow *window)
+window_overlaps_focus_window (MetaWindow *window,
+                              int         new_x,
+                              int         new_y)
 {
   MetaWindow *focus_window;
   MtkRectangle window_frame, focus_frame, overlap;
@@ -363,6 +365,9 @@ window_overlaps_focus_window (MetaWindow *window)
     return FALSE;
 
   meta_window_get_frame_rect (window, &window_frame);
+  window_frame.x = new_x;
+  window_frame.y = new_y;
+
   meta_window_get_frame_rect (focus_window, &focus_frame);
 
   return mtk_rectangle_intersect (&window_frame,
@@ -414,7 +419,7 @@ avoid_being_obscured_as_second_modal_dialog (MetaWindow    *window,
 #ifdef HAVE_X11_CLIENT
       meta_window_x11_same_application (window, focus_window) &&
 #endif
-      window_overlaps_focus_window (window))
+      window_overlaps_focus_window (window, *x, *y))
     {
       find_most_freespace (window, focus_window, *x, *y, x, y);
       meta_topic (META_DEBUG_PLACEMENT,
@@ -987,7 +992,7 @@ meta_window_place (MetaWindow        *window,
       g_assert (focus_window != NULL);
 
       /* No need to do anything if the window doesn't overlap at all */
-      found_fit = !window_overlaps_focus_window (window);
+      found_fit = !window_overlaps_focus_window (window, x, y);
 
       /* Try to do a first fit again, this time only taking into account the
        * focus window.
diff --git a/src/core/window.c b/src/core/window.c
index 3c690fa36..d6e8406be 100644
--- a/src/core/window.c
+++ b/src/core/window.c
@@ -2284,8 +2284,8 @@ meta_window_show (MetaWindow *window)
   if (focus_window &&
       window->showing_for_first_time &&
       !meta_window_is_ancestor_of_transient (focus_window, window) &&
-      ((!place_on_top_on_map && !takes_focus_on_map) ||
-       window_would_be_covered_by_always_above_window (window)))
+      !place_on_top_on_map &&
+      !takes_focus_on_map)
     {
       needs_stacking_adjustment = TRUE;
       if (!window->placed)
@@ -2316,6 +2316,12 @@ meta_window_show (MetaWindow *window)
       meta_window_force_placement (window, place_flags);
     }
 
+  if (focus_window &&
+      window->showing_for_first_time &&
+      !meta_window_is_ancestor_of_transient (focus_window, window) &&
+      window_would_be_covered_by_always_above_window (window))
+    needs_stacking_adjustment = TRUE;
+
   if (needs_stacking_adjustment)
     {
       gboolean overlap;
diff --git a/src/tests/meson.build b/src/tests/meson.build
index 1194cb006..6b5048490 100644
--- a/src/tests/meson.build
+++ b/src/tests/meson.build
@@ -726,6 +726,7 @@ stacking_tests = [
   'workspace-basic',
   'workspace-test',
   'always-on-top',
+  'always-on-top-map-new-maximized',
   'focus-default-window-globally-active-input',
   'workspace-unmanaging-window',
   'click-to-focus-and-raise',
@@ -739,7 +740,8 @@ stacking_tests = [
   'sticky',
   'sticky-modals',
   'sticky-transients',
-  'strut-monitor-changes'
+  'strut-monitor-changes',
+  'window-placement',
 ]
 
 foreach stacking_test: stacking_tests
diff --git a/src/tests/stacking/always-on-top-map-new-maximized.metatest b/src/tests/stacking/always-on-top-map-new-maximized.metatest
new file mode 100644
index 000000000..f93307082
--- /dev/null
+++ b/src/tests/stacking/always-on-top-map-new-maximized.metatest
@@ -0,0 +1,20 @@
+resize_monitor default 400 400
+
+new_client w wayland
+create w/1 csd
+resize w/1 350 350
+show w/1
+move w/1 25 25
+make_above w/1 true
+
+assert_focused w/1
+assert_stacking w/1
+
+# Map a maximized window; it should not gain focus due to being mostly covered.
+
+create w/2 csd
+maximize w/2
+show w/2
+
+assert_focused w/1
+assert_stacking w/2 w/1
diff --git a/src/tests/stacking/window-placement.metatest b/src/tests/stacking/window-placement.metatest
new file mode 100644
index 000000000..00634a31a
--- /dev/null
+++ b/src/tests/stacking/window-placement.metatest
@@ -0,0 +1,84 @@
+new_client w wayland
+resize_monitor default 250 250
+set_pref center-new-windows false
+
+# Show 4 windows in a row and assert that they are placed in a grid and focused
+# correctly.
+
+create w/1 csd
+resize w/1 100 100
+show w/1
+
+assert_focused w/1
+assert_position w/1 24 16
+assert_size w/1 100 100
+
+create w/2 csd
+resize w/2 100 100
+show w/2
+
+assert_focused w/2
+assert_position w/2 24 116
+assert_size w/2 100 100
+
+create w/3 csd
+resize w/3 100 100
+show w/3
+
+assert_focused w/3
+assert_position w/3 124 16
+assert_size w/3 100 100
+
+create w/4 csd
+resize w/4 100 100
+show w/4
+
+assert_focused w/4
+assert_position w/4 124 116
+assert_size w/4 100 100
+
+destroy w/1
+destroy w/2
+destroy w/3
+destroy w/4
+wait
+
+assert_stacking
+
+
+# Show 1 window, make it 'always-on-top' and make sure the following windows
+# still get placed and focused correctly.
+
+create w/1 csd
+resize w/1 100 100
+show w/1
+
+assert_focused w/1
+assert_position w/1 24 16
+assert_size w/1 100 100
+
+make_above w/1 true
+
+create w/2 csd
+resize w/2 100 100
+show w/2
+
+assert_focused w/2
+assert_position w/2 24 116
+assert_size w/2 100 100
+
+create w/3 csd
+resize w/3 100 100
+show w/3
+
+assert_focused w/3
+assert_position w/3 124 16
+assert_size w/3 100 100
+
+create w/4 csd
+resize w/4 100 100
+show w/4
+
+assert_focused w/4
+assert_position w/4 124 116
+assert_size w/4 100 100