diff --git a/src/util/taproot.rs b/src/util/taproot.rs
index dd843193..0330d93d 100644
--- a/src/util/taproot.rs
+++ b/src/util/taproot.rs
@@ -20,6 +20,7 @@ use io;
 use secp256k1::{self, Secp256k1};
 
 use core::fmt;
+use core::cmp::Reverse;
 #[cfg(feature = "std")]
 use std::error;
 
@@ -210,9 +211,9 @@ impl TaprootSpendInfo {
         I: IntoIterator<Item = (u64, Script)>,
         C: secp256k1::Verification,
     {
-        let mut node_weights = BinaryHeap::<(u64, NodeInfo)>::new();
+        let mut node_weights = BinaryHeap::<(Reverse<u128>, NodeInfo)>::new();
         for (p, leaf) in script_weights {
-            node_weights.push((p, NodeInfo::new_leaf_with_ver(leaf, LeafVersion::default())));
+            node_weights.push((Reverse(p as u128), NodeInfo::new_leaf_with_ver(leaf, LeafVersion::default())));
         }
         if node_weights.is_empty() {
             return Err(TaprootBuilderError::IncompleteTree);
@@ -222,7 +223,10 @@ impl TaprootSpendInfo {
             let (p1, s1) = node_weights.pop().expect("len must be at least two");
             let (p2, s2) = node_weights.pop().expect("len must be at least two");
             // Insert the sum of first two in the tree as a new node
-            let p = p1.checked_add(p2).ok_or(TaprootBuilderError::ScriptWeightOverflow)?;
+            // N.B.: p1 + p2 can never actually saturate as you would need to have 2**64 max u64s
+            // from the input to overflow. However, saturating is a reasonable behavior here as
+            // huffman tree construction would treat all such elements as "very likely".
+            let p = Reverse(p1.0.saturating_add(p2.0));
             node_weights.push((p, NodeInfo::combine(s1, s2)?));
         }
         // Every iteration of the loop reduces the node_weights.len() by exactly 1
@@ -803,8 +807,6 @@ pub enum TaprootBuilderError {
     IncompleteTree,
     /// Called finalize on a empty tree
     EmptyTree,
-    /// Script weight overflow
-    ScriptWeightOverflow,
 }
 
 impl fmt::Display for TaprootBuilderError {
@@ -832,9 +834,6 @@ impl fmt::Display for TaprootBuilderError {
             TaprootBuilderError::EmptyTree => {
                 write!(f, "Called finalize on an empty tree")
             }
-            TaprootBuilderError::ScriptWeightOverflow => {
-                write!(f, "Script weight overflow in Huffman tree construction")
-            },
         }
     }
 }