diff --git a/lib/matplotlib/contour.py b/lib/matplotlib/contour.py
index 77dc58740971..1bb09df44685 100644
--- a/lib/matplotlib/contour.py
+++ b/lib/matplotlib/contour.py
@@ -1029,8 +1029,12 @@ def _process_contour_level_args(self, args, z_dtype):
 
         if self.filled and len(self.levels) < 2:
             raise ValueError("Filled contours require at least 2 levels.")
-        if len(self.levels) > 1 and np.min(np.diff(self.levels)) <= 0.0:
-            raise ValueError("Contour levels must be increasing")
+
+        # check if filled contours are monotonically increasing:
+        if (self.filled and len(self.levels) > 1 and
+                np.any(np.diff(self.levels) <= 0)):
+            raise ValueError(
+                "Filled contour levels must be monotonically increasing")
 
     def _process_levels(self):
         """
@@ -1496,7 +1500,7 @@ def _initialize_x_y(self, z):
     *n*=7 is the default.
 
     If array-like, draw contour lines at the specified levels.
-    The values must be in increasing order.
+    For filled contours, the values must be in increasing order.
 
     If not specified, a reasonable default is automatically chosen. For
     linear scales, this corresponds to *levels=7*. For logarithmic
@@ -1519,8 +1523,8 @@ def _initialize_x_y(self, z):
     The colors of the levels, i.e. the lines for `.contour` and the
     areas for `.contourf`.
 
-    The sequence is cycled for the levels in ascending order. If the
-    sequence is shorter than the number of levels, it's repeated.
+    The colors are mapped to the levels in the order specified, repeating as
+    necessary if there are fewer colors than levels.
 
     As a shortcut, a single color may be used in place of one-element lists, i.e.
     ``'red'`` instead of ``['red']`` to color all levels with the same color.
@@ -1641,8 +1645,8 @@ def _initialize_x_y(self, z):
 
     If a number, all levels will be plotted with this linewidth.
 
-    If a sequence, the levels in ascending order will be plotted with
-    the linewidths in the order specified.
+    If a sequence, the linewidths are mapped to the levels in order,
+    repeating as necessary if there are fewer linewidths than levels.
 
     If None, this falls back to :rc:`lines.linewidth`.
 
diff --git a/lib/matplotlib/tests/test_contour.py b/lib/matplotlib/tests/test_contour.py
index e242c219df10..54f821e94823 100644
--- a/lib/matplotlib/tests/test_contour.py
+++ b/lib/matplotlib/tests/test_contour.py
@@ -335,6 +335,22 @@ def test_contourf_decreasing_levels():
         plt.contourf(z, [1.0, 0.0])
 
 
+@check_figures_equal()
+def test_contour_decreasing_levels(fig_ref, fig_test):
+    # Check that contour works with decreasing levels:
+    Z = np.arange(100).reshape(10, 10)
+    ax_ref = fig_ref.subplots()
+    ax_test = fig_test.subplots()
+
+    levels0 = np.array([6, 10, 20, 30, 33, 53, 80])
+    colors0 = ['red', 'green', 'blue', 'cyan', 'magenta', 'yellow', 'black']
+
+    # sorted:
+    ax_ref.contour(Z, levels=levels0, colors=np.array(colors0))
+    # reversed:
+    ax_test.contour(Z, levels=levels0[::-1], colors=colors0[::-1])
+
+
 def test_contourf_symmetric_locator():
     # github issue 7271
     z = np.arange(12).reshape((3, 4))