diff --git a/core/src/fixed.rs b/core/src/fixed.rs
index 3488c00..625b77c 100644
--- a/core/src/fixed.rs
+++ b/core/src/fixed.rs
@@ -138,6 +138,16 @@ impl<const SHIFT: u32> Fixed<SHIFT> {
         Self(narrow(shift_round(self.0 as i64 * by.0 as i64, BY)))
     }
 
+    /// A part of a span that is often nothing: no part of nothing is
+    /// nothing, for the cost of a comparison rather than a widening
+    /// multiply and a rounding.
+    pub const fn scaled<const BY: u32>(self, by: Fixed<BY>) -> Self {
+        match self.0 == 0 {
+            true => self,
+            false => self.mul(by),
+        }
+    }
+
     /// Repeated a whole number of times, which no grid rounds.
     pub const fn mul_int(self, by: i32) -> Self {
         Self(narrow(self.0 as i64 * by as i64))
@@ -179,7 +189,7 @@ impl<const SHIFT: u32> Fixed<SHIFT> {
     /// `from` and `to` a fraction of the way apart, the fraction being the
     /// receiver -- the argument order [`crate::util::LerpUtil`] already uses.
     pub const fn lerp<const OF: u32>(self, from: Fixed<OF>, to: Fixed<OF>) -> Fixed<OF> {
-        from.add(to.sub(from).mul(self))
+        from.add(to.sub(from).scaled(self))
     }
 
     pub const fn min(self, other: Self) -> Self {
diff --git a/core/src/ui/render_state.rs b/core/src/ui/render_state.rs
index 8d4c15a..5cfc0a6 100644
--- a/core/src/ui/render_state.rs
+++ b/core/src/ui/render_state.rs
@@ -1146,9 +1146,9 @@ impl AxisRemap {
             true => offset,
             false => offset / scale.extent,
         };
-        let from_px = scale.from_px + scale.from_px_span.mul(fraction);
-        let to_rel = scale.to_rel + scale.to_rel_span.mul(fraction);
-        let to_px = scale.to_px + scale.to_px_span.mul(fraction);
+        let from_px = scale.from_px + scale.from_px_span.scaled(fraction);
+        let to_rel = scale.to_rel + scale.to_rel_span.scaled(fraction);
+        let to_px = scale.to_px + scale.to_px_span.scaled(fraction);
         Len::from_parts(to_rel, scalar.px - from_px + to_px)
     }
 }