diff --git a/conrod_core/src/mesh.rs b/conrod_core/src/mesh.rs
index 74929a41c..74050f470 100644
--- a/conrod_core/src/mesh.rs
+++ b/conrod_core/src/mesh.rs
@@ -206,11 +206,15 @@ impl Mesh {
             let (w, h) = rect.w_h();
             let left = (rect.left() * dpi_factor + half_viewport_w).round() as i32;
             let top = (rect.top() * dpi_factor - half_viewport_h).round().abs() as i32;
-            let width = (w * dpi_factor).round() as u32;
-            let height = (h * dpi_factor).round() as u32;
-            Scizzor {
-                top_left: [left.max(0), top.max(0)],
-                dimensions: [width.min(viewport_w as u32), height.min(viewport_h as u32)],
+            let width = ((w * dpi_factor).round() as u32).min(viewport_w as u32);
+            let height = ((h * dpi_factor).round() as u32).min(viewport_h as u32);
+            if width == 0 || height == 0 {
+                None
+            } else {
+                Some(Scizzor {
+                    top_left: [left.max(0), top.max(0)],
+                    dimensions: [width, height],
+                })
             }
         };
 
@@ -257,7 +261,9 @@ impl Mesh {
 
                 // Update the scizzor and produce a command.
                 current_scizzor = new_scizzor;
-                commands.push(PreparedCommand::Scizzor(new_scizzor));
+                if let Some(scizzor) = new_scizzor {
+                    commands.push(PreparedCommand::Scizzor(scizzor));
+                }
 
                 // Set the state back to plain drawing.
                 current_state = State::Plain {
@@ -265,6 +271,11 @@ impl Mesh {
                 };
             }
 
+            // If the scizzor is `None`, then nothing is viewable, so don't draw anything.
+            if current_scizzor.is_none() {
+                continue;
+            }
+
             match kind {
                 render::PrimitiveKind::Rectangle { color } => {
                     switch_to_plain_state!();
diff --git a/conrod_core/src/position/range.rs b/conrod_core/src/position/range.rs
index f0ad449c9..828a55489 100644
--- a/conrod_core/src/position/range.rs
+++ b/conrod_core/src/position/range.rs
@@ -236,12 +236,7 @@ impl Range {
 
     /// The Range that represents the range of the overlap between two Ranges if there is some.
     ///
-    /// Note that If one end of `self` aligns exactly with the opposite end of `other`, `Some`
-    /// `Range` will be returned with a magnitude of `0.0`. This is useful for algorithms that
-    /// involve calculating the visibility of widgets, as it allows for including widgets whose
-    /// bounding box may be a one dimensional straight line.
-    ///
-    /// The returned `Range`'s `start` will always be <= its `end`.
+    /// The returned `Range`'s `start` will always be < its `end`.
     ///
     /// # Examples
     ///
@@ -266,7 +261,7 @@ impl Range {
         let start = ::utils::partial_max(self.start, other.start);
         let end = ::utils::partial_min(self.end, other.end);
         let magnitude = end - start;
-        if magnitude >= 0.0 {
+        if magnitude > 0.0 {
             Some(Range::new(start, end))
         } else {
             None
diff --git a/conrod_core/src/render.rs b/conrod_core/src/render.rs
index bd86d0bdc..0ec661f63 100644
--- a/conrod_core/src/render.rs
+++ b/conrod_core/src/render.rs
@@ -942,7 +942,7 @@ fn next_widget<'a>(
         }
 
         // We only want to return primitives that are actually visible.
-        let is_visible = container.rect.overlap(window_rect).is_some()
+        let is_visible = container.rect.overlap(scizzor).is_some()
             && graph::algo::cropped_area_of_widget(graph, id).is_some();
         if !is_visible {
             continue;
diff --git a/conrod_core/src/widget/primitive/line.rs b/conrod_core/src/widget/primitive/line.rs
index 7f0e8b2a5..c0f673664 100644
--- a/conrod_core/src/widget/primitive/line.rs
+++ b/conrod_core/src/widget/primitive/line.rs
@@ -65,6 +65,8 @@ pub enum Cap {
     Round,
 }
 
+const DEFAULT_THICKNESS: Scalar = 1.0;
+
 impl Line {
     /// Build a new **Line** widget with the given style.
     pub fn styled(start: Point, end: Point, style: Style) -> Self {
@@ -93,8 +95,9 @@ impl Line {
 
     /// The same as [**Line::abs**](./struct.Line#method.abs) but with the given style.
     pub fn abs_styled(start: Point, end: Point, style: Style) -> Self {
-        let (xy, dim) = Rect::from_corners(start, end).xy_dim();
-        Line::styled(start, end, style).wh(dim).xy(xy)
+        let line = Line::styled(start, end, style);
+        let (xy, wh) = line.calc_rect().xy_dim();
+        Line::styled(start, end, style).wh(wh).xy(xy)
     }
 
     /// Build a new **Line** and shift the location of the start and end points so that the centre
@@ -112,10 +115,10 @@ impl Line {
 
     /// The same as [**Line::centred**](./struct.Line#method.centred) but with the given style.
     pub fn centred_styled(start: Point, end: Point, style: Style) -> Self {
-        let dim = Rect::from_corners(start, end).dim();
-        let mut line = Line::styled(start, end, style).wh(dim);
+        let mut line = Line::styled(start, end, style);
         line.should_centre_points = true;
-        line
+        let r = line.calc_rect();
+        line.wh(r.dim())
     }
 
     /// The thickness or width of the Line.
@@ -144,6 +147,12 @@ impl Line {
         self.style.set_pattern(Pattern::Dotted);
         self
     }
+
+    fn calc_rect(&self) -> Rect {
+        let thickness = self.style.maybe_thickness.unwrap_or(DEFAULT_THICKNESS);
+        let corners = rect_corners(self.start, self.end, thickness * 0.5);
+        super::bounding_box_for_points(corners.iter().cloned())
+    }
 }
 
 impl Style {
@@ -241,7 +250,6 @@ impl Style {
 
     /// The width or thickness of the Line.
     pub fn get_thickness(&self, theme: &Theme) -> Scalar {
-        const DEFAULT_THICKNESS: Scalar = 1.0;
         self.maybe_thickness
             .or_else(|| {
                 theme