diff --git a/src/state.rs b/src/state.rs
index 063cf051..80bdb2ec 100644
--- a/src/state.rs
+++ b/src/state.rs
@@ -385,19 +385,20 @@ Outcome:
                 let ideal_height = IDEAL_TARGET_SIZE * ROW_COUNT as i32;
                 let ideal_height_px = (ideal_height * density).ceil().0 as u32;
 
+                let max_wide_height = Rational {
+                    numerator: 172,
+                    denominator: 540,
+                };
+                let ideal_panel_height = Rational {
+                    numerator: ideal_height_px as i32,
+                    denominator: dbg!(px_size.width),
+                };
                 // Reduce height to match what the layout can fill.
-                // For this, we need to guess if normal or wide will be picked up.
+                // For this, we need to guess if normal or wide will be picked.
                 // This must match `eek_gtk_keyboard.c::get_type`.
                 // TODO: query layout database and choose one directly
-                let abstract_width
-                    = PixelSize {
-                        scale_factor: output.scale as u32,
-                        pixels: px_size.width,
-                    } 
-                    .as_scaled_ceiling();
-
                 let (arrangement, height_as_widths) = {
-                    if abstract_width < 540 {(
+                    if max_wide_height < dbg!(ideal_panel_height) {(
                         ArrangementKind::Base,
                         Rational {
                             numerator: 210,
@@ -405,16 +406,13 @@ Outcome:
                         },
                     )} else {(
                         ArrangementKind::Wide,
-                        Rational {
-                            numerator: 172,
-                            denominator: 540,
-                        }
+                        max_wide_height,
                     )}
                 };
 
                 let height
                     = cmp::min(
-                        ideal_height_px,
+                        dbg!(ideal_height_px),
                         (height_as_widths * px_size.width as i32).ceil() as u32,
                     );
 
@@ -755,4 +753,33 @@ pub mod test {
             )),
         );
     }
+    
+    
+    #[test]
+    fn size_l5_scale1() {
+        use crate::outputs::{Mode, Geometry, c, Size};
+        assert_eq!(
+            Application::get_preferred_height_and_arrangement(&OutputState {
+                current_mode: Some(Mode {
+                    width: 720,
+                    height: 1440,
+                }),
+                geometry: Some(Geometry{
+                    transform: c::Transform::Normal,
+                    phys_size: Size {
+                        width: Some(Millimeter(65)),
+                        height: Some(Millimeter(130)),
+                    },
+                }),
+                scale: 1,
+            }),
+            Some((
+                PixelSize {
+                    scale_factor: 1,
+                    pixels: 420,
+                },
+                ArrangementKind::Base,
+            )),
+        );
+    }
 }
diff --git a/src/util.rs b/src/util.rs
index 0b99ea88..d96f69e6 100644
--- a/src/util.rs
+++ b/src/util.rs
@@ -4,6 +4,7 @@ use std::rc::Rc;
 use crate::float_ord::FloatOrd;
 
 use std::borrow::Borrow;
+use std::cmp::{Ordering, PartialOrd};
 use std::hash::{ Hash, Hasher };
 use std::ops::Mul;
 
@@ -242,6 +243,34 @@ impl<U, T: Mul<U, Output=T>> Mul<Rational<U>> for Rational<T> {
     }
 }
 
+impl PartialEq for Rational<i32> {
+    fn eq(&self, other: &Self) -> bool {
+        (self.denominator as i64).saturating_mul(other.numerator as i64)
+            == (other.denominator as i64).saturating_mul(self.numerator as i64)
+    }
+}
+
+impl Eq for Rational<i32> {}
+
+impl Ord for Rational<i32> {
+    fn cmp(&self, other: &Self) -> Ordering {
+        // Using 64-bit values to make overflows unlikely.
+        // If i32_max * u32_max can exceed i64_max,
+        // then this is actually PartialOrd.
+        // Saturating mul used just to avoid propagating mistakes.
+        (other.denominator as i64).saturating_mul(self.numerator as i64)
+            .cmp(
+                &(self.denominator as i64).saturating_mul(other.numerator as i64)
+             )
+    }
+}
+
+impl PartialOrd for Rational<i32> {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
 /// Compares pointers but not internal values of Rc
 pub struct Pointer<T>(pub Rc<T>);
 
@@ -327,4 +356,20 @@ mod tests {
             vec![(5, 0), (6, 0), (7, 0), (5, 1), (6, 1), (7, 1), (5, 2)]
         );
     }
+    
+    #[test]
+    fn check_rational_cmp() {
+        assert_eq!(
+            Rational { numerator: 1, denominator: 1 },
+            Rational { numerator: 1, denominator: 1 },
+        );
+        assert_eq!(
+            Rational { numerator: 1, denominator: 1 },
+            Rational { numerator: 2, denominator: 2 },
+        );
+        assert!(
+            Rational { numerator: 1, denominator: 1 }
+            < Rational { numerator: 2, denominator: 1 }
+        );
+    }
 }