diff --git a/rich/align.py b/rich/align.py
index d98d3c00..b1f9b3bb 100644
--- a/rich/align.py
+++ b/rich/align.py
@@ -142,8 +142,7 @@ class Align(JupyterMixin):
             Constrain(
                 self.renderable, width if self.width is None else min(width, self.width)
             ),
-            options
-            # options.update(height=self.height or options.height or 1),
+            options.update(height=None),
         )
         lines = list(Segment.split_lines(rendered))
         width, height = Segment.get_shape(lines)
diff --git a/rich/console.py b/rich/console.py
index ca937e61..122f3c21 100644
--- a/rich/console.py
+++ b/rich/console.py
@@ -134,6 +134,8 @@ class ConsoleOptions:
     """True if the target is a terminal, otherwise False."""
     encoding: str
     """Encoding of terminal."""
+    max_height: int
+    """Height of container (starts as terminal)"""
     justify: Optional[JustifyMethod] = None
     """Justify value override for renderable."""
     overflow: Optional[OverflowMethod] = None
@@ -145,7 +147,6 @@ class ConsoleOptions:
     markup: Optional[bool] = None
     """Enable markup when rendering strings."""
     height: Optional[int] = None
-    """Height available, or None for no height limit."""
 
     @property
     def ascii_only(self) -> bool:
@@ -194,6 +195,8 @@ class ConsoleOptions:
         if not isinstance(markup, NoChange):
             options.markup = markup
         if not isinstance(height, NoChange):
+            if height is not None:
+                options.max_height = height
             options.height = None if height is None else max(0, height)
         return options
 
@@ -223,6 +226,7 @@ class ConsoleOptions:
         options = self.copy()
         options.min_width = options.max_width = max(0, width)
         options.height = height
+        options.max_height = height
         return options
 
 
@@ -907,6 +911,7 @@ class Console:
     def options(self) -> ConsoleOptions:
         """Get default console options."""
         return ConsoleOptions(
+            max_height=self.size.height,
             size=self.size,
             legacy_windows=self.legacy_windows,
             min_width=1,
diff --git a/tests/test_box.py b/tests/test_box.py
index f235a82e..21ba4fd0 100644
--- a/tests/test_box.py
+++ b/tests/test_box.py
@@ -44,6 +44,7 @@ def test_box_substitute():
         max_width=100,
         is_terminal=True,
         encoding="utf-8",
+        max_height=25,
     )
     assert HEAVY.substitute(options) == SQUARE
 
diff --git a/tests/test_console.py b/tests/test_console.py
index 771c07f9..3874d450 100644
--- a/tests/test_console.py
+++ b/tests/test_console.py
@@ -66,6 +66,7 @@ def test_truecolor_terminal():
 def test_console_options_update():
     options = ConsoleOptions(
         ConsoleDimensions(80, 25),
+        max_height=25,
         legacy_windows=False,
         min_width=10,
         max_width=20,
diff --git a/tests/test_live_render.py b/tests/test_live_render.py
index 3a56fdd3..e8ae1108 100644
--- a/tests/test_live_render.py
+++ b/tests/test_live_render.py
@@ -31,6 +31,7 @@ def test_restore_cursor(live_render):
 def test_rich_console(live_render):
     options = ConsoleOptions(
         ConsoleDimensions(80, 25),
+        max_height=25,
         legacy_windows=False,
         min_width=10,
         max_width=20,
diff --git a/tests/test_padding.py b/tests/test_padding.py
index d4508e9f..7ab0d741 100644
--- a/tests/test_padding.py
+++ b/tests/test_padding.py
@@ -40,6 +40,7 @@ def test_rich_console():
     style = Style(color="red")
     options = ConsoleOptions(
         ConsoleDimensions(80, 25),
+        max_height=25,
         legacy_windows=False,
         min_width=10,
         max_width=20,