diff --git a/src/gtkutil.c b/src/gtkutil.c
index a6bba096a4..167329ccb8 100644
--- a/src/gtkutil.c
+++ b/src/gtkutil.c
@@ -1174,6 +1182,7 @@ xg_frame_set_char_size (struct frame *f, int width, int height)
   int outer_width = width + FRAME_TOOLBAR_WIDTH (f);
   bool was_visible = false;
   bool hide_child_frame;
+  int scale = xg_get_scale (f);
 
 #ifndef HAVE_PGTK
   gtk_window_get_size (GTK_WINDOW (FRAME_GTK_OUTER_WIDGET (f)),
@@ -1196,8 +1206,42 @@ xg_frame_set_char_size (struct frame *f, int width, int height)
   /* Do this before resize, as we don't know yet if we will be resized.  */
   FRAME_RIF (f)->clear_under_internal_border (f);
 
-  outer_height /= xg_get_scale (f);
-  outer_width /= xg_get_scale (f);
+  outer_height /= scale;
+  outer_width /= scale;
+
+  if (scale != 1 && !frame_resize_pixelwise)
+    {
+      int base_width_unscaled = (FRAME_TEXT_COLS_TO_PIXEL_WIDTH (f, 1)
+				 + FRAME_TOOLBAR_WIDTH (f));
+      int base_width_scaled = base_width_unscaled / scale;
+      int base_height_unscaled = (FRAME_TEXT_LINES_TO_PIXEL_HEIGHT (f, 1)
+				  + FRAME_MENUBAR_HEIGHT (f)
+				  + FRAME_TOOLBAR_HEIGHT (f));
+      int base_height_scaled = base_height_unscaled / scale;
+      int width_inc = FRAME_COLUMN_WIDTH (f) / scale;
+      int height_inc = FRAME_LINE_HEIGHT (f) / scale;
+      int width_rest, height_rest;
+
+      if (width_inc < 1)
+	width_inc = 1;
+
+      if (height_inc < 1)
+	height_inc = 1;
+
+      if (outer_width < base_width_scaled)
+	outer_width = base_width_scaled;
+
+      if (outer_height < base_height_scaled)
+	outer_height = base_height_scaled;
+
+      width_rest = (outer_width - base_width_scaled) % width_inc;
+      height_rest = (outer_height - base_height_scaled) % height_inc;
+
+      if (width_rest > 0 || (base_width_unscaled % scale) > 0)
+	outer_width = outer_width + width_inc - width_rest;
+      if (height_rest > 0 || (base_height_unscaled % scale) > 0)
+	outer_height = outer_height + height_inc - height_rest;
+    }
 
   xg_wm_set_size_hint (f, 0, 0);