(x_draw_fringe_bitmap) [USE_TOOLKIT_SCROLL_BARS]:

Extend fringe background to scroll bar gap.
(x_scroll_bar_create) [USE_TOOLKIT_SCROLL_BARS]:
Set bar->fringe_extended_p.
(XTset_vertical_scroll_bar) [USE_TOOLKIT_SCROLL_BARS]:
Put leftmost/rightmost scroll bars on frame edge.  Check fringe
background extension.  Don't clear extended fringe background area.

src/xterm.c

@@ -720,8 +720,10 @@ x_draw_fringe_bitmap (w, row, p)
   else
     x_clip_to_row (w, row, -1, gc);
 
-  if (p->bx >= 0 && !p->overlay_p)
+  if (!p->overlay_p)
     {
+      int bx = p->bx, by = p->by, nx = p->nx, ny = p->ny;
+
       /* In case the same realized face is used for fringes and
 	 for something displayed in the text (e.g. face `region' on
 	 mono-displays, the fill style may have been changed to
@@ -731,8 +733,55 @@ x_draw_fringe_bitmap (w, row, p)
       else
 	XSetForeground (display, face->gc, face->background);
 
-      XFillRectangle (display, window, face->gc,
-		      p->bx, p->by, p->nx, p->ny);
+#ifdef USE_TOOLKIT_SCROLL_BARS
+      /* If the fringe is adjacent to the left (right) scroll bar of a
+	 leftmost (rightmost, respectively) window, then extend its
+	 background to the gap between the fringe and the bar.  */
+      if ((WINDOW_LEFTMOST_P (w)
+	   && WINDOW_HAS_VERTICAL_SCROLL_BAR_ON_LEFT (w))
+	  || (WINDOW_RIGHTMOST_P (w)
+	      && WINDOW_HAS_VERTICAL_SCROLL_BAR_ON_RIGHT (w)))
+	{
+	  int sb_width = WINDOW_CONFIG_SCROLL_BAR_WIDTH (w);
+
+	  if (sb_width > 0)
+	    {
+	      int left = WINDOW_SCROLL_BAR_AREA_X (w);
+	      int width = (WINDOW_CONFIG_SCROLL_BAR_COLS (w)
+			   * FRAME_COLUMN_WIDTH (f));
+
+	      if (bx < 0)
+		{
+		  /* Bitmap fills the fringe.  */
+		  if (left + width == p->x)
+		    bx = left + sb_width;
+		  else if (p->x + p->wd == left)
+		    bx = left;
+		  if (bx >= 0)
+		    {
+		      int header_line_height = WINDOW_HEADER_LINE_HEIGHT (w);
+
+		      nx = width - sb_width;
+		      by = WINDOW_TO_FRAME_PIXEL_Y (w, max (header_line_height,
+							    row->y));
+		      ny = row->visible_height;
+		    }
+		}
+	      else
+		{
+		  if (left + width == bx)
+		    {
+		      bx = left + sb_width;
+		      nx += width - sb_width;
+		    }
+		  else if (bx + nx == left)
+		    nx += width - sb_width;
+		}
+	    }
+	}
+#endif
+      if (bx >= 0 && nx > 0)
+	XFillRectangle (display, window, face->gc, bx, by, nx, ny);
 
       if (!face->stipple)
 	XSetForeground (display, face->gc, face->foreground);
@@ -4787,6 +4836,9 @@ x_scroll_bar_create (w, top, left, width, height)
   XSETINT (bar->start, 0);
   XSETINT (bar->end, 0);
   bar->dragging = Qnil;
+#ifdef USE_TOOLKIT_SCROLL_BARS
+  bar->fringe_extended_p = Qnil;
+#endif
 
   /* Add bar to its frame's list of scroll bars.  */
   bar->next = FRAME_SCROLL_BARS (f);
@@ -4979,6 +5031,9 @@ XTset_vertical_scroll_bar (w, portion, whole, position)
   struct scroll_bar *bar;
   int top, height, left, sb_left, width, sb_width;
   int window_y, window_height;
+#ifdef USE_TOOLKIT_SCROLL_BARS
+  int fringe_extended_p;
+#endif
 
   /* Get window dimensions.  */
   window_box (w, -1, 0, &window_y, 0, &window_height);
@@ -4999,15 +5054,9 @@ XTset_vertical_scroll_bar (w, portion, whole, position)
   /* Compute the left edge of the scroll bar.  */
 #ifdef USE_TOOLKIT_SCROLL_BARS
   if (WINDOW_HAS_VERTICAL_SCROLL_BAR_ON_RIGHT (w))
-    sb_left = (left +
-	       (WINDOW_RIGHTMOST_P (w)
-		? width - sb_width - (width - sb_width) / 2
-		: 0));
+    sb_left = left + (WINDOW_RIGHTMOST_P (w) ? width - sb_width : 0);
   else
-    sb_left = (left +
-	       (WINDOW_LEFTMOST_P (w)
-		? (width - sb_width) / 2
-		: width - sb_width));
+    sb_left = left + (WINDOW_LEFTMOST_P (w) ? 0 : width - sb_width);
 #else
   if (WINDOW_HAS_VERTICAL_SCROLL_BAR_ON_RIGHT (w))
     sb_left = left + width - sb_width;
@@ -5015,14 +5064,33 @@ XTset_vertical_scroll_bar (w, portion, whole, position)
     sb_left = left;
 #endif
 
+#ifdef USE_TOOLKIT_SCROLL_BARS
+  if (WINDOW_HAS_VERTICAL_SCROLL_BAR_ON_LEFT (w))
+    fringe_extended_p = (WINDOW_LEFTMOST_P (w)
+			 && WINDOW_LEFT_FRINGE_WIDTH (w)
+			 && (WINDOW_HAS_FRINGES_OUTSIDE_MARGINS (w)
+			     || WINDOW_LEFT_MARGIN_COLS (w) == 0));
+  else
+    fringe_extended_p = (WINDOW_RIGHTMOST_P (w)
+			 && WINDOW_RIGHT_FRINGE_WIDTH (w)
+			 && (WINDOW_HAS_FRINGES_OUTSIDE_MARGINS (w)
+			     || WINDOW_RIGHT_MARGIN_COLS (w) == 0));
+#endif
+
   /* Does the scroll bar exist yet?  */
   if (NILP (w->vertical_scroll_bar))
     {
       if (width > 0 && height > 0)
 	{
 	  BLOCK_INPUT;
-	  x_clear_area (FRAME_X_DISPLAY (f), FRAME_X_WINDOW (f),
-			left, top, width, height, False);
+#ifdef USE_TOOLKIT_SCROLL_BARS
+	  if (fringe_extended_p)
+	    x_clear_area (FRAME_X_DISPLAY (f), FRAME_X_WINDOW (f),
+			  sb_left, top, sb_width, height, False);
+	  else
+#endif
+	    x_clear_area (FRAME_X_DISPLAY (f), FRAME_X_WINDOW (f),
+			  left, top, width, height, False);
 	  UNBLOCK_INPUT;
 	}
 
@@ -5049,13 +5117,19 @@ XTset_vertical_scroll_bar (w, portion, whole, position)
 #ifdef USE_TOOLKIT_SCROLL_BARS
 
       /* Move/size the scroll bar widget.  */
-      if (mask)
+      if (mask || !NILP (bar->fringe_extended_p) != fringe_extended_p)
 	{
 	  /* Since toolkit scroll bars are smaller than the space reserved
 	     for them on the frame, we have to clear "under" them.  */
 	  if (width > 0 && height > 0)
-	    x_clear_area (FRAME_X_DISPLAY (f), FRAME_X_WINDOW (f),
-                          left, top, width, height, False);
+	    {
+	      if (fringe_extended_p)
+		x_clear_area (FRAME_X_DISPLAY (f), FRAME_X_WINDOW (f),
+			      sb_left, top, sb_width, height, False);
+	      else
+		x_clear_area (FRAME_X_DISPLAY (f), FRAME_X_WINDOW (f),
+			      left, top, width, height, False);
+	    }
 #ifdef USE_GTK
           xg_update_scrollbar_pos (f,
                                    SCROLL_BAR_X_WINDOW (bar),
@@ -5130,6 +5204,8 @@ XTset_vertical_scroll_bar (w, portion, whole, position)
     }
 
 #ifdef USE_TOOLKIT_SCROLL_BARS
+  bar->fringe_extended_p = fringe_extended_p ? Qt : Qnil;
+
   x_set_toolkit_scroll_bar_thumb (bar, portion, position, whole);
 #else /* not USE_TOOLKIT_SCROLL_BARS */
   /* Set the scroll bar's current state, unless we're currently being