diff --git a/examples/lines_bars_and_markers/markevery_demo.py b/examples/lines_bars_and_markers/markevery_demo.py
index 62eda10de3bc..d917fa01501b 100644
--- a/examples/lines_bars_and_markers/markevery_demo.py
+++ b/examples/lines_bars_and_markers/markevery_demo.py
@@ -36,39 +36,39 @@
 # define the figure size and grid layout properties
 figsize = (10, 8)
 cols = 3
-gs = gridspec.GridSpec(len(cases) // cols + 1, cols)
-gs.update(hspace=0.4)
+rows = len(cases) // cols + 1
 # define the data for cartesian plots
 delta = 0.11
 x = np.linspace(0, 10 - 2 * delta, 200) + delta
 y = np.sin(x) + 1.0 + delta
 
+
+def trim_axs(axs, N):
+    """little helper to massage the axs list to have correct length..."""
+    axs = axs.flat
+    for ax in axs[N:]:
+        ax.remove()
+    return axs[:N]
+
 ###############################################################################
 # Plot each markevery case for linear x and y scales
 
-fig1 = plt.figure(num=1, figsize=figsize)
-ax = []
-for i, case in enumerate(cases):
-    row = (i // cols)
-    col = i % cols
-    ax.append(fig1.add_subplot(gs[row, col]))
-    ax[-1].set_title('markevery=%s' % str(case))
-    ax[-1].plot(x, y, 'o', ls='-', ms=4, markevery=case)
+fig1, axs = plt.subplots(rows, cols, figsize=figsize, constrained_layout=True)
+axs = trim_axs(axs, len(cases))
+for ax, case in zip(axs, cases):
+    ax.set_title('markevery=%s' % str(case))
+    ax.plot(x, y, 'o', ls='-', ms=4, markevery=case)
 
 ###############################################################################
 # Plot each markevery case for log x and y scales
 
-fig2 = plt.figure(num=2, figsize=figsize)
-axlog = []
-for i, case in enumerate(cases):
-    row = (i // cols)
-    col = i % cols
-    axlog.append(fig2.add_subplot(gs[row, col]))
-    axlog[-1].set_title('markevery=%s' % str(case))
-    axlog[-1].set_xscale('log')
-    axlog[-1].set_yscale('log')
-    axlog[-1].plot(x, y, 'o', ls='-', ms=4, markevery=case)
-fig2.tight_layout()
+fig2, axs = plt.subplots(rows, cols, figsize=figsize, constrained_layout=True)
+axs = trim_axs(axs, len(cases))
+for ax, case in zip(axs, cases):
+    ax.set_title('markevery=%s' % str(case))
+    ax.set_xscale('log')
+    ax.set_yscale('log')
+    ax.plot(x, y, 'o', ls='-', ms=4, markevery=case)
 
 ###############################################################################
 # Plot each markevery case for linear x and y scales but zoomed in
@@ -76,17 +76,13 @@
 # it is always interpreted with respect to the first data point which might be
 # different to the first visible data point.
 
-fig3 = plt.figure(num=3, figsize=figsize)
-axzoom = []
-for i, case in enumerate(cases):
-    row = (i // cols)
-    col = i % cols
-    axzoom.append(fig3.add_subplot(gs[row, col]))
-    axzoom[-1].set_title('markevery=%s' % str(case))
-    axzoom[-1].plot(x, y, 'o', ls='-', ms=4, markevery=case)
-    axzoom[-1].set_xlim((6, 6.7))
-    axzoom[-1].set_ylim((1.1, 1.7))
-fig3.tight_layout()
+fig3, axs = plt.subplots(rows, cols, figsize=figsize, constrained_layout=True)
+axs = trim_axs(axs, len(cases))
+for ax, case in zip(axs, cases):
+    ax.set_title('markevery=%s' % str(case))
+    ax.plot(x, y, 'o', ls='-', ms=4, markevery=case)
+    ax.set_xlim((6, 6.7))
+    ax.set_ylim((1.1, 1.7))
 
 # define data for polar plots
 r = np.linspace(0, 3.0, 200)
@@ -95,14 +91,11 @@
 ###############################################################################
 # Plot each markevery case for polar plots
 
-fig4 = plt.figure(num=4, figsize=figsize)
-axpolar = []
-for i, case in enumerate(cases):
-    row = (i // cols)
-    col = i % cols
-    axpolar.append(fig4.add_subplot(gs[row, col], projection='polar'))
-    axpolar[-1].set_title('markevery=%s' % str(case))
-    axpolar[-1].plot(theta, r, 'o', ls='-', ms=4, markevery=case)
-fig4.tight_layout()
+fig4, axs = plt.subplots(rows, cols, figsize=figsize,
+        subplot_kw={'projection': 'polar'}, constrained_layout=True)
+axs = trim_axs(axs, len(cases))
+for ax, case in zip(axs, cases):
+    ax.set_title('markevery=%s' % str(case))
+    ax.plot(theta, r, 'o', ls='-', ms=4, markevery=case)
 
 plt.show()
diff --git a/lib/matplotlib/spines.py b/lib/matplotlib/spines.py
index 042bf84d4bfc..a20e71bc5448 100644
--- a/lib/matplotlib/spines.py
+++ b/lib/matplotlib/spines.py
@@ -159,6 +159,8 @@ def get_window_extent(self, renderer=None):
         # correct:
         self._adjust_location()
         bb = super().get_window_extent(renderer=renderer)
+        if self.axis is None:
+            return bb
         bboxes = [bb]
         tickstocheck = [self.axis.majorTicks[0]]
         if len(self.axis.minorTicks) > 1:
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 45384d6b30fa..cf3ae1448e7d 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -6271,6 +6271,14 @@ def test_minor_accountedfor():
                            atol=1e-2)
 
 
+def test_get_tightbbox_polar():
+    fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})
+    fig.canvas.draw()
+    bb = ax.get_tightbbox(fig.canvas.get_renderer())
+    assert_allclose(bb.extents,
+        [107.7778,  29.2778, 539.7847, 450.7222], rtol=1e-03)
+
+
 @check_figures_equal(extensions=["png"])
 def test_axis_bool_arguments(fig_test, fig_ref):
     # Test if False and "off" give the same