diff --git a/src/branch_and_bound.rs b/src/branch_and_bound.rs
index 256ac5e..954e44e 100644
--- a/src/branch_and_bound.rs
+++ b/src/branch_and_bound.rs
@@ -142,6 +142,8 @@ pub fn select_coins_bnb(
     let mut index_selection: Vec<usize> = vec![];
     let mut best_selection: Option<Vec<usize>> = None;
 
+    let upper_bound = target.checked_add(cost_of_change)?;
+
     // Create a tuple of (effective_value, waste, weighted_utxo)
     // * filter out effective values and wastes that are None
     // * filter out negative effective values
@@ -237,7 +239,7 @@ pub fn select_coins_bnb(
         // it's high fee_rate environment.  During low fee environments, a utxo may
         // have negative waste, therefore adding more utxos in such an environment
         // may still result in reduced waste.
-        else if value > target.unchecked_add(cost_of_change) //TODO we can check this for overflow
+        else if value > upper_bound //TODO we can check this for overflow
                                                              //before the loop begins by adding
                                                              //target to utxo_pool sum.
             || current_waste > best_waste && fee_rate > long_term_fee_rate
@@ -707,4 +709,29 @@ mod tests {
         );
         assert!(list.is_none());
     }
+
+    #[test]
+    fn upper_bound_overflow() {
+        // the upper_bound is target + cost_of_change.
+        // adding these two together returns NONE on overflow.
+        let target = Amount::MAX;
+        let cost_of_change = Amount::MAX;
+
+        let satisfaction_weight = Weight::from_wu(204);
+        let mut weighted_utxos = vec![
+            WeightedUtxo {
+                satisfaction_weight,
+                utxo: TxOut { value: target, script_pubkey: ScriptBuf::new() },
+            },
+        ];
+
+        let list = select_coins_bnb(
+            target,
+            cost_of_change,
+            FeeRate::ZERO,
+            FeeRate::ZERO,
+            &mut weighted_utxos,
+        );
+        assert!(list.is_none());
+    }
 }