diff --git a/sandbox/uber.css b/sandbox/uber.css
index f27e16262..7739d920b 100644
--- a/sandbox/uber.css
+++ b/sandbox/uber.css
@@ -1,7 +1,8 @@
 #uber1 {
   /* border: heavy green; */
-  layout: horizontal;
-  text: on green;
+  layout: vertical;
+  text: on dark_green;
+  overflow-y: scroll;
 }
 
 .list-item {
@@ -9,18 +10,17 @@
 
   /* height: 8; */
   margin: 1 2;
+  text: on dark_blue;
 }
 
 #child1 {
-  text: on blue;
 }
 
 #child2 {
-  text: on magenta;
 }
 
-#uber2 {
+/* #uber2 {
   margin: 3;
   layout: dock;
   docks: _default=left;
-}
+} */
diff --git a/sandbox/uber.py b/sandbox/uber.py
index 1115f7d33..ecb28455c 100644
--- a/sandbox/uber.py
+++ b/sandbox/uber.py
@@ -20,7 +20,12 @@ class BasicApp(App):
         self.mount(
             uber1=Widget(
                 Placeholder(id="child1", classes={"list-item"}),
-                Widget(id="child2", classes={"list-item"}),
+                Placeholder(id="child2", classes={"list-item"}),
+                Placeholder(id="child3", classes={"list-item"}),
+                Placeholder(classes={"list-item"}),
+                Placeholder(classes={"list-item"}),
+                Placeholder(classes={"list-item"}),
+                Placeholder(classes={"list-item"}),
                 # Placeholder(id="child3", classes={"list-item"}),
             ),
             # uber2=uber2,
diff --git a/src/textual/_compositor.py b/src/textual/_compositor.py
index f309f76dc..2240256f1 100644
--- a/src/textual/_compositor.py
+++ b/src/textual/_compositor.py
@@ -207,10 +207,7 @@ class Compositor:
                 placements, arranged_widgets = widget.layout.arrange(
                     widget, region.size, scroll
                 )
-                for placement in placements:
-                    log(placement=placement)
 
-                log(arranged=arranged_widgets)
                 widgets.update(arranged_widgets)
                 placements = sorted(placements, key=attrgetter("order"))
 
@@ -226,8 +223,6 @@ class Compositor:
             return total_region.size
 
         virtual_size = add_widget(root, size.region, (), size.region)
-        # for widget, placement in map.items():
-        #     log("*", widget, placement)
         return map, virtual_size, widgets
 
     async def mount_all(self, screen: Screen) -> None:
@@ -319,9 +314,7 @@ class Compositor:
 
         for region, order, clip in self.map.values():
             region = region.intersection(clip)
-            log(clipped=region, bool=bool(region and (region in screen_region)))
             if region and (region in screen_region):
-                log(1)
                 region_cuts = (region.x, region.x + region.width)
                 for cut in cuts[region.y : region.y + region.height]:
                     cut.extend(region_cuts)
@@ -372,13 +365,17 @@ class Compositor:
     @classmethod
     def _assemble_chops(
         cls, chops: list[dict[int, list[Segment] | None]]
-    ) -> Iterable[Iterable[Segment]]:
+    ) -> list[list[Segment]]:
 
-        from_iterable = chain.from_iterable
-        for bucket in chops:
-            yield from_iterable(
-                line for _, line in sorted(bucket.items()) if line is not None
+        # Pretty sure we don't need to sort the buck items
+        segment_lines = [
+            sum(
+                (line for _, line in bucket.items() if line is not None),
+                start=[],
             )
+            for bucket in chops
+        ]
+        return segment_lines
 
     def render(
         self,
@@ -406,9 +403,11 @@ class Compositor:
 
         # Maps each cut on to a list of segments
         cuts = self.cuts
+        # dict.fromkeys is a callable which takes a list of ints returns a dict which maps ints on to a list of Segments or None.
         fromkeys = cast(
             Callable[[list[int]], dict[int, list[Segment] | None]], dict.fromkeys
         )
+        # A mapping of cut index to a list of segments for each line
         chops: list[dict[int, list[Segment] | None]] = [
             fromkeys(cut_set) for cut_set in cuts
         ]
@@ -431,18 +430,21 @@ class Compositor:
                 final_cuts = [cut for cut in cuts[y] if (last_cut >= cut >= first_cut)]
 
                 if len(final_cuts) == 2:
+                    # Two cuts, which means the entire line
                     cut_segments = [line]
                 else:
+                    # More than one cut, which means we need to divide the line
                     render_x = render_region.x
                     relative_cuts = [cut - render_x for cut in final_cuts]
                     _, *cut_segments = divide(line, relative_cuts)
+                # Since we are painting front to back, the first segments for a cut "wins"
                 for cut, segments in zip(final_cuts, cut_segments):
                     if chops[y][cut] is None:
                         chops[y][cut] = segments
 
         # Assemble the cut renders in to lists of segments
         crop_x, crop_y, crop_x2, crop_y2 = crop_region.corners
-        output_lines = self._assemble_chops(chops[crop_y:crop_y2])
+        render_lines = self._assemble_chops(chops[crop_y:crop_y2])
 
         def width_view(line: list[Segment]) -> list[Segment]:
             if line:
@@ -451,9 +453,7 @@ class Compositor:
             return line
 
         if crop is not None and (crop_x, crop_x2) != (0, self.width):
-            render_lines = [width_view(line) for line in output_lines]
-        else:
-            render_lines = list(output_lines)
+            render_lines = [width_view(line) for line in render_lines]
 
         return SegmentLines(render_lines, new_lines=True)
 
@@ -463,14 +463,21 @@ class Compositor:
         yield self.render(console)
 
     def update_widget(self, console: Console, widget: Widget) -> LayoutUpdate | None:
+        """Update a given widget in the composition.
+
+        Args:
+            console (Console): Console instance.
+            widget (Widget): Widget to update.
+
+        Returns:
+            LayoutUpdate | None: A renderable or None if nothing to render.
+        """
         if widget not in self.regions:
             return None
 
         region, clip = self.regions[widget]
-
-        if not region.size:
+        if not region:
             return None
-
         update_region = region.intersection(clip)
         if not update_region:
             return None
diff --git a/src/textual/css/_styles_builder.py b/src/textual/css/_styles_builder.py
index f4137abe3..b15215856 100644
--- a/src/textual/css/_styles_builder.py
+++ b/src/textual/css/_styles_builder.py
@@ -12,6 +12,7 @@ from .constants import (
     VALID_BOX_SIZING,
     VALID_EDGE,
     VALID_DISPLAY,
+    VALID_OVERFLOW,
     VALID_VISIBILITY,
 )
 from .errors import DeclarationError
@@ -20,7 +21,7 @@ from .scalar import Scalar, ScalarOffset, Unit, ScalarError
 from .styles import DockGroup, Styles
 from .tokenize import Token
 from .transition import Transition
-from .types import BoxSizing, Edge, Display, Visibility
+from .types import BoxSizing, Edge, Display, Overflow, Visibility
 from .._duration import _duration_as_seconds
 from .._easing import EASING
 from ..geometry import Spacing, SpacingDimensions, clamp
@@ -83,6 +84,40 @@ class StylesBuilder:
             except Exception as error:
                 self.error(declaration.name, declaration.token, str(error))
 
+    def _process_enum(
+        self, name: str, tokens: list[Token], valid_values: set[str]
+    ) -> str:
+        """Process a declaration that expects an enum.
+
+        Args:
+            name (str): Name of declaration.
+            tokens (list[Token]): Tokens from parser.
+            valid_values (list[str]): A set of valid values.
+
+        Returns:
+            bool: True if the value is valid or False if it is invalid (also generates an error)
+        """
+
+        if len(tokens) != 1:
+            self.error(name, tokens[0], "expected a single token here")
+            return False
+
+        token = tokens[0]
+        token_name, value, _, _, location, _ = token
+        if token_name != "token":
+            self.error(
+                name,
+                token,
+                f"invalid token {value!r}, expected {friendly_list(valid_values)}",
+            )
+        if value not in valid_values:
+            self.error(
+                name,
+                token,
+                f"invalid value {value!r} for {name}, expected {friendly_list(valid_values)}",
+            )
+        return value
+
     def process_display(self, name: str, tokens: list[Token], important: bool) -> None:
         for token in tokens:
             name, value, _, _, location, _ = token
@@ -153,6 +188,20 @@ class StylesBuilder:
     ) -> None:
         self._process_scalar(name, tokens)
 
+    def process_overflow_x(
+        self, name: str, tokens: list[Token], important: bool
+    ) -> None:
+        self.styles._rules["overflow_x"] = cast(
+            Overflow, self._process_enum(name, tokens, VALID_OVERFLOW)
+        )
+
+    def process_overflow_y(
+        self, name: str, tokens: list[Token], important: bool
+    ) -> None:
+        self.styles._rules["overflow_y"] = cast(
+            Overflow, self._process_enum(name, tokens, VALID_OVERFLOW)
+        )
+
     def process_visibility(
         self, name: str, tokens: list[Token], important: bool
     ) -> None:
diff --git a/src/textual/css/constants.py b/src/textual/css/constants.py
index 2fa415997..adeba8731 100644
--- a/src/textual/css/constants.py
+++ b/src/textual/css/constants.py
@@ -25,6 +25,7 @@ VALID_EDGE: Final = {"top", "right", "bottom", "left"}
 VALID_LAYOUT: Final = {"dock", "vertical", "grid"}
 
 VALID_BOX_SIZING: Final = {"border-box", "content-box"}
+VALID_OVERFLOW: Final = {"scroll", "hidden", "auto"}
 
 
 NULL_SPACING: Final = Spacing(0, 0, 0, 0)
diff --git a/src/textual/css/styles.py b/src/textual/css/styles.py
index 37c51b426..d180bb932 100644
--- a/src/textual/css/styles.py
+++ b/src/textual/css/styles.py
@@ -13,7 +13,7 @@ from rich.style import Style
 
 from .. import log
 from .._animator import Animation, EasingFunction
-from ..geometry import Region, Size, Spacing
+from ..geometry import Size, Spacing
 from ._style_properties import (
     BorderProperty,
     BoxProperty,
@@ -32,11 +32,19 @@ from ._style_properties import (
     TransitionsProperty,
     FractionalProperty,
 )
-from .constants import VALID_BOX_SIZING, VALID_DISPLAY, VALID_VISIBILITY
+from .constants import VALID_BOX_SIZING, VALID_DISPLAY, VALID_VISIBILITY, VALID_OVERFLOW
 from .scalar import Scalar, ScalarOffset, Unit
 from .scalar_animation import ScalarAnimation
 from .transition import Transition
-from .types import BoxSizing, Display, Edge, Specificity3, Specificity4, Visibility
+from .types import (
+    BoxSizing,
+    Display,
+    Edge,
+    Overflow,
+    Specificity3,
+    Specificity4,
+    Visibility,
+)
 
 if sys.version_info >= (3, 8):
     from typing import TypedDict
@@ -92,6 +100,9 @@ class RulesMap(TypedDict, total=False):
     dock: str
     docks: tuple[DockGroup, ...]
 
+    overflow_x: Overflow
+    overflow_y: Overflow
+
     layers: tuple[str, ...]
     layer: str
 
@@ -161,6 +172,9 @@ class StylesBase(ABC):
     dock = DockProperty()
     docks = DocksProperty()
 
+    overflow_x = StringEnumProperty(VALID_OVERFLOW, "hidden")
+    overflow_y = StringEnumProperty(VALID_OVERFLOW, "hidden")
+
     layer = NameProperty()
     layers = NameListProperty()
     transitions = TransitionsProperty()
@@ -638,6 +652,11 @@ class Styles(StylesBase):
             if has_rule("text_style"):
                 append_declaration("text-style", str(get_rule("text_style")))
 
+        if has_rule("overflow-x"):
+            append_declaration("overflow-x", self.overflow_x)
+        if has_rule("overflow-y"):
+            append_declaration("overflow-y", self.overflow_y)
+
         if has_rule("box-sizing"):
             append_declaration("box-sizing", self.box_sizing)
         if has_rule("width"):
diff --git a/src/textual/css/types.py b/src/textual/css/types.py
index da170922c..9c257657b 100644
--- a/src/textual/css/types.py
+++ b/src/textual/css/types.py
@@ -16,6 +16,7 @@ Edge = Literal["top", "right", "bottom", "left"]
 Visibility = Literal["visible", "hidden", "initial", "inherit"]
 Display = Literal["block", "none"]
 BoxSizing = Literal["border-box", "content-box"]
+Overflow = Literal["scroll", "hidden", "auto"]
 EdgeStyle = Tuple[str, Color]
 Specificity3 = Tuple[int, int, int]
 Specificity4 = Tuple[int, int, int, int]
diff --git a/src/textual/layouts/vertical.py b/src/textual/layouts/vertical.py
index 4d964d99d..197359c53 100644
--- a/src/textual/layouts/vertical.py
+++ b/src/textual/layouts/vertical.py
@@ -35,7 +35,7 @@ class VerticalLayout(Layout):
             region = Region(margin.left, y + margin.top, content_width, content_height)
             max_width = max(max_width, content_width + margin.width)
             add_placement(WidgetPlacement(region, widget, 0))
-            y += region.y_max
+            y += region.height + margin.top
             max_height = y + margin.bottom
 
         total_region = Region(0, 0, max_width, max_height)
diff --git a/src/textual/widget.py b/src/textual/widget.py
index 6e001a3f6..1b023c956 100644
--- a/src/textual/widget.py
+++ b/src/textual/widget.py
@@ -121,8 +121,6 @@ class Widget(DOMNode):
         """
 
         renderable = self.render()
-        self.log(renderable)
-
         styles = self.styles
 
         parent_text_style = self.parent.text_style