diff --git a/lib/matplotlib/tests/test_tightlayout.py b/lib/matplotlib/tests/test_tightlayout.py
index f7e571958610..0516971d2d9c 100644
--- a/lib/matplotlib/tests/test_tightlayout.py
+++ b/lib/matplotlib/tests/test_tightlayout.py
@@ -272,3 +272,41 @@ def test_empty_layout():
 
     fig = plt.gcf()
     fig.tight_layout()
+
+
+def test_verybig_decorators_horizontal():
+    "Test that warning emitted when xlabel too big"
+    fig, ax = plt.subplots(figsize=(3, 2))
+    ax.set_xlabel('a' * 100)
+    with warnings.catch_warnings(record=True) as w:
+        fig.tight_layout()
+        assert len(w) == 1
+
+
+def test_verybig_decorators_vertical():
+    "Test that warning emitted when xlabel too big"
+    fig, ax = plt.subplots(figsize=(3, 2))
+    ax.set_ylabel('a' * 100)
+    with warnings.catch_warnings(record=True) as w:
+        fig.tight_layout()
+        assert len(w) == 1
+
+
+def test_big_decorators_horizontal():
+    "Test that warning emitted when xlabel too big"
+    fig, axs = plt.subplots(1, 2, figsize=(3, 2))
+    axs[0].set_xlabel('a' * 30)
+    axs[1].set_xlabel('b' * 30)
+    with warnings.catch_warnings(record=True) as w:
+        fig.tight_layout()
+        assert len(w) == 1
+
+
+def test_big_decorators_vertical():
+    "Test that warning emitted when xlabel too big"
+    fig, axs = plt.subplots(2, 1, figsize=(3, 2))
+    axs[0].set_ylabel('a' * 20)
+    axs[1].set_ylabel('b' * 20)
+    with warnings.catch_warnings(record=True) as w:
+        fig.tight_layout()
+        assert len(w) == 1
diff --git a/lib/matplotlib/tight_layout.py b/lib/matplotlib/tight_layout.py
index 21823f9aea38..1c18dc63c30d 100644
--- a/lib/matplotlib/tight_layout.py
+++ b/lib/matplotlib/tight_layout.py
@@ -171,25 +171,46 @@ def auto_adjust_subplotpars(
         margin_bottom = max([sum(s) for s in vspaces[-cols:]] + [0])
         margin_bottom += pad_inches / fig_height_inch
 
+    if margin_left + margin_right >= 1:
+        margin_left = 0.4999
+        margin_right = 0.4999
+        warnings.warn('The left and right margins cannot be made large '
+                      'enough to accommodate all axes decorations. ')
+    if margin_bottom + margin_top >= 1:
+        margin_bottom = 0.4999
+        margin_top = 0.4999
+        warnings.warn('The bottom and top margins cannot be made large '
+                      'enough to accommodate all axes decorations. ')
+
     kwargs = dict(left=margin_left,
                   right=1 - margin_right,
                   bottom=margin_bottom,
                   top=1 - margin_top)
-
     if cols > 1:
         hspace = (
             max(sum(s)
                 for i in range(rows)
                 for s in hspaces[i * (cols + 1) + 1:(i + 1) * (cols + 1) - 1])
             + hpad_inches / fig_width_inch)
+        # axes widths:
         h_axes = (1 - margin_right - margin_left - hspace * (cols - 1)) / cols
-        kwargs["wspace"] = hspace / h_axes
+        if h_axes < 0:
+            warnings.warn('tight_layout cannot make axes width small enough '
+                          'to accommodate all axes decorations')
+            kwargs["wspace"] = 0.5
+        else:
+            kwargs["wspace"] = hspace / h_axes
 
     if rows > 1:
         vspace = (max(sum(s) for s in vspaces[cols:-cols])
                   + vpad_inches / fig_height_inch)
         v_axes = (1 - margin_top - margin_bottom - vspace * (rows - 1)) / rows
-        kwargs["hspace"] = vspace / v_axes
+        if v_axes < 0:
+            warnings.warn('tight_layout cannot make axes height small enough '
+                          'to accommodate all axes decorations')
+            kwargs["hspace"] = 0.5
+        else:
+            kwargs["hspace"] = vspace / v_axes
 
     return kwargs