diff --git a/news/88.bugfix.md b/news/88.bugfix.md
new file mode 100644
index 00000000..69de7fa6
--- /dev/null
+++ b/news/88.bugfix.md
@@ -0,0 +1 @@
+Fix `Table.set_column_max_width()` having no effect on rendered tables
diff --git a/src/cleo/ui/table.py b/src/cleo/ui/table.py
index 2651bb51..da2a3410 100644
--- a/src/cleo/ui/table.py
+++ b/src/cleo/ui/table.py
@@ -104,7 +104,7 @@ def set_column_widths(self, widths: list[int]) -> Table:
         return self
 
     def set_column_max_width(self, column_index: int, width: int) -> Table:
-        self._column_widths[column_index] = width
+        self._column_max_widths[column_index] = width
 
         return self
 
@@ -426,8 +426,10 @@ def _build_table_rows(self, rows: Rows) -> Iterator[Row | TableSeparator]:
                 if column in self._column_max_widths and self._column_max_widths[
                     column
                 ] < len(self._io.remove_format(cell)):
-                    assert isinstance(self._io, Output)
-                    cell = self._io.formatter.format_and_wrap(
+                    output = (
+                        self._io if isinstance(self._io, Output) else self._io.output
+                    )
+                    cell = output.formatter.format_and_wrap(
                         cell, self._column_max_widths[column] * colspan
                     )
 
diff --git a/tests/ui/test_table.py b/tests/ui/test_table.py
index d10b60c2..3901b114 100644
--- a/tests/ui/test_table.py
+++ b/tests/ui/test_table.py
@@ -481,3 +481,46 @@ def test_style_for_side_effects(io: BufferedIO) -> None:
     output2 = io.fetch_output()
 
     assert output1 != output2
+
+
+def test_column_max_width_wraps_long_cells(io: BufferedIO) -> None:
+    table = Table(io)
+    table.set_headers(["ISBN", "Description"])
+    table.set_rows(
+        [["99921-58-10-7", "A long description that has to be wrapped to fit"]]
+    )
+    table.set_column_max_width(1, 12)
+
+    table.render()
+
+    expected = """\
++---------------+--------------+
+| ISBN          | Description  |
++---------------+--------------+
+| 99921-58-10-7 | A long descr |
+|               | iption that  |
+|               | has to be wr |
+|               | apped to fit |
++---------------+--------------+
+"""
+
+    assert io.fetch_output() == expected
+
+
+def test_column_max_width_does_not_widen_short_cells(io: BufferedIO) -> None:
+    table = Table(io)
+    table.set_headers(["ISBN", "Title"])
+    table.set_rows([["99921-58-10-7", "Divine Comedy"]])
+    table.set_column_max_width(1, 40)
+
+    table.render()
+
+    expected = """\
++---------------+---------------+
+| ISBN          | Title         |
++---------------+---------------+
+| 99921-58-10-7 | Divine Comedy |
++---------------+---------------+
+"""
+
+    assert io.fetch_output() == expected