diff --git a/lib/matplotlib/backends/backend_gtk3.py b/lib/matplotlib/backends/backend_gtk3.py
index 2f34248837dc..60537cf6443a 100644
--- a/lib/matplotlib/backends/backend_gtk3.py
+++ b/lib/matplotlib/backends/backend_gtk3.py
@@ -436,10 +436,21 @@ def set_window_title(self, title):
 
     def resize(self, width, height):
         """Set the canvas size in pixels."""
-        #_, _, cw, ch = self.canvas.allocation
-        #_, _, ww, wh = self.window.allocation
-        #self.window.resize (width-cw+ww, height-ch+wh)
-        self.window.resize(width, height)
+        if self.toolbar:
+            toolbar_size = self.toolbar.size_request()
+            height += toolbar_size.height
+        if self.statusbar:
+            statusbar_size = self.statusbar.size_request()
+            height += statusbar_size.height
+        canvas_size = self.canvas.get_allocation()
+        if canvas_size.width == canvas_size.height == 1:
+            # A canvas size of (1, 1) cannot exist in most cases, because
+            # window decorations would prevent such a small window. This call
+            # must be before the window has been mapped and widgets have been
+            # sized, so just change the window's starting size.
+            self.window.set_default_size(width, height)
+        else:
+            self.window.resize(width, height)
 
 
 class NavigationToolbar2GTK3(NavigationToolbar2, Gtk.Toolbar):
diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
index 69b22df4528d..299e893993f8 100644
--- a/lib/matplotlib/figure.py
+++ b/lib/matplotlib/figure.py
@@ -442,6 +442,9 @@ def _set_dpi(self, dpi, forward=True):
         forward : bool
             Passed on to `~.Figure.set_size_inches`
         """
+        if dpi == self._dpi:
+            # We don't want to cause undue events in backends.
+            return
         self._dpi = dpi
         self.dpi_scale_trans.clear().scale(dpi)
         w, h = self.get_size_inches()
diff --git a/lib/matplotlib/tests/test_backend_qt.py b/lib/matplotlib/tests/test_backend_qt.py
index 1f4798e25498..2545c3c68923 100644
--- a/lib/matplotlib/tests/test_backend_qt.py
+++ b/lib/matplotlib/tests/test_backend_qt.py
@@ -271,4 +271,5 @@ def crashing_callback(fig, stale):
     fig.stale_callback = crashing_callback
     # this should not raise
     canvas = FigureCanvasQTAgg(fig)
+    fig.stale = True
     assert called