diff --git a/PerfectNumbers.Core/UInt128Extensions.cs b/PerfectNumbers.Core/UInt128Extensions.cs
index bfc18d7..c55e483 100644
--- a/PerfectNumbers.Core/UInt128Extensions.cs
+++ b/PerfectNumbers.Core/UInt128Extensions.cs
@@ -677,15 +677,25 @@ public static class UInt128Extensions
         //     return UInt128.Zero;
         // }
 
-        value %= modulus;
-        addend %= modulus;
-        if (addend == UInt128.Zero)
-        {
-            return value;
-        }
+        // value and addend already lie below the modulus throughout the divisor-by-divisor CPU flow,
+        // so skip the redundant reductions the old helper performed.
+        // value %= modulus;
+        // addend %= modulus;
+        // Odd moduli keep 2^delta from landing on zero, leaving this branch inactive in the scan.
+        // if (addend == UInt128.Zero)
+        // {
+        //     return value;
+        // }
 
         UInt128 threshold = modulus - addend;
-        return value >= threshold ? value - threshold : value + addend;
+        if (value >= threshold)
+        {
+            return value - threshold;
+        }
+
+        UInt128 sum = value + addend;
+        // The sum stays below the modulus under the threshold guard above, so no wraparound occurs.
+        return sum;
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
diff --git a/PerfectNumbers.Core/ULongExtensions.cs b/PerfectNumbers.Core/ULongExtensions.cs
index dd8e040..2de1e01 100644
--- a/PerfectNumbers.Core/ULongExtensions.cs
+++ b/PerfectNumbers.Core/ULongExtensions.cs
@@ -464,17 +464,20 @@ public static partial class ULongExtensions
 		// 	return 0UL;
 		// }
 
+		// The Pollard Rho walks keep both operands below the modulus, so skip re-folding them here.
 		UInt128 sum = (UInt128)value + addend;
-		UInt128 mod = modulus;
-		if (sum >= mod)
+		if (sum < modulus)
 		{
-			sum -= mod;
-			if (sum >= mod)
-			{
-				sum -= mod;
-			}
+			return (ulong)sum;
 		}
 
+		sum -= modulus;
+		// After one subtraction the sum always falls below the modulus on this path, making the old guard redundant.
+		// if (sum >= modulus)
+		// {
+		// 	sum -= modulus;
+		// }
+
 		return (ulong)sum;
 	}