diff --git a/bitcoin/src/blockdata/block.rs b/bitcoin/src/blockdata/block.rs
index 88971c608..f83cb413e 100644
--- a/bitcoin/src/blockdata/block.rs
+++ b/bitcoin/src/blockdata/block.rs
@@ -10,7 +10,7 @@
 use core::fmt;
 
 use hashes::{sha256d, HashEngine};
-use internals::compact_size;
+use internals::{compact_size, ToU64};
 use io::{BufRead, Write};
 
 use super::Weight;
@@ -263,7 +263,7 @@ impl BlockCheckedExt for Block<Checked> {
     fn weight(&self) -> Weight {
         // This is the exact definition of a weight unit, as defined by BIP-141 (quote above).
         let wu = block_base_size(self.transactions()) * 3 + self.total_size();
-        Weight::from_wu_usize(wu)
+        Weight::from_wu(wu.to_u64())
     }
 
     fn total_size(&self) -> usize {
diff --git a/bitcoin/src/blockdata/transaction.rs b/bitcoin/src/blockdata/transaction.rs
index 897475a2e..1fdc4af40 100644
--- a/bitcoin/src/blockdata/transaction.rs
+++ b/bitcoin/src/blockdata/transaction.rs
@@ -343,7 +343,7 @@ impl TransactionExt for Transaction {
     fn weight(&self) -> Weight {
         // This is the exact definition of a weight unit, as defined by BIP-141 (quote above).
         let wu = self.base_size() * 3 + self.total_size();
-        Weight::from_wu_usize(wu)
+        Weight::from_wu(wu.to_u64())
     }
 
     fn base_size(&self) -> usize {
@@ -1142,7 +1142,9 @@ impl InputWeightPrediction {
     ///
     /// See also [`InputWeightPrediction::total_weight`]
     pub const fn witness_weight(&self) -> Weight {
-        Weight::from_wu_usize(self.script_size * 4 + self.witness_size)
+        let wu = self.script_size * 4 + self.witness_size;
+        let wu = wu as u64; // Can't use `ToU64` in const context.
+        Weight::from_wu(wu)
     }
 }
 
diff --git a/units/src/weight.rs b/units/src/weight.rs
index 4e0b5026d..8c8827df7 100644
--- a/units/src/weight.rs
+++ b/units/src/weight.rs
@@ -48,9 +48,6 @@ impl Weight {
     /// Constructs a new [`Weight`] from weight units.
     pub const fn from_wu(wu: u64) -> Self { Weight(wu) }
 
-    /// Constructs a new [`Weight`] from usize weight units.
-    pub const fn from_wu_usize(wu: usize) -> Self { Weight(wu as u64) }
-
     /// Constructs a new [`Weight`] from kilo weight units returning [`None`] if an overflow occurred.
     pub fn from_kwu(wu: u64) -> Option<Self> { wu.checked_mul(1000).map(Weight) }
 
@@ -254,7 +251,6 @@ mod tests {
     #[test]
     fn weight_constructor() {
         assert_eq!(Weight::ZERO, Weight::from_wu(0));
-        assert_eq!(Weight::ZERO, Weight::from_wu_usize(0_usize));
     }
 
     #[test]