diff --git a/units/src/amount/mod.rs b/units/src/amount/mod.rs
index 7fb8bc535..940b9a5a8 100644
--- a/units/src/amount/mod.rs
+++ b/units/src/amount/mod.rs
@@ -39,6 +39,7 @@ pub use self::{
     signed::SignedAmount,
     unsigned::Amount,
 };
+pub(crate) use self::result::OptionExt;
 
 /// A set of denominations in which amounts can be expressed.
 ///
diff --git a/units/src/amount/result.rs b/units/src/amount/result.rs
index ae1c6e12d..4b78d0080 100644
--- a/units/src/amount/result.rs
+++ b/units/src/amount/result.rs
@@ -1,7 +1,6 @@
 // SPDX-License-Identifier: CC0-1.0
 
-//! Provides a monodic numeric result type that is used to return the result of
-//! doing mathematical operations (`core::ops`) on amount types.
+//! Provides a monodic type used when mathematical operations (`core::ops`) return an amount type.
 
 use core::{fmt, ops};
 
@@ -378,7 +377,7 @@ impl<'a> core::iter::Sum<&'a NumOpResult<SignedAmount>> for NumOpResult<SignedAm
     }
 }
 
-pub(in crate::amount) trait OptionExt<T> {
+pub(crate) trait OptionExt<T> {
     fn valid_or_error(self) -> NumOpResult<T>;
 }
 
diff --git a/units/src/fee.rs b/units/src/fee.rs
index 1bb3b9b66..39dff63b0 100644
--- a/units/src/fee.rs
+++ b/units/src/fee.rs
@@ -13,6 +13,7 @@
 
 use core::ops;
 
+use crate::amount::{NumOpResult, OptionExt};
 use crate::{Amount, FeeRate, Weight};
 
 impl Amount {
@@ -160,17 +161,15 @@ impl FeeRate {
 
 /// Computes the ceiling so that the fee computation is conservative.
 impl ops::Mul<FeeRate> for Weight {
-    type Output = Amount;
+    type Output = NumOpResult<Amount>;
 
-    fn mul(self, rhs: FeeRate) -> Self::Output {
-        Amount::from_sat((rhs.to_sat_per_kwu() * self.to_wu() + 999) / 1000)
-    }
+    fn mul(self, rhs: FeeRate) -> Self::Output { rhs.checked_mul_by_weight(self).valid_or_error() }
 }
 
 impl ops::Mul<Weight> for FeeRate {
-    type Output = Amount;
+    type Output = NumOpResult<Amount>;
 
-    fn mul(self, rhs: Weight) -> Self::Output { rhs * self }
+    fn mul(self, rhs: Weight) -> Self::Output { self.checked_mul_by_weight(rhs).valid_or_error() }
 }
 
 impl ops::Div<Weight> for Amount {
@@ -265,7 +264,7 @@ mod tests {
         let three = Weight::from_vb(3).unwrap();
         let six = Amount::from_sat_unchecked(6);
 
-        assert_eq!(two * three, six);
+        assert_eq!(two * three, six.into());
     }
 
     #[test]