diff --git a/policy.go b/policy.go
index a0f78b33..8f4585f5 100644
--- a/policy.go
+++ b/policy.go
@@ -26,11 +26,14 @@ const (
 func calcMinRequiredTxRelayFee(serializedSize int64, minRelayTxFee btcutil.Amount) int64 {
 	// Calculate the minimum fee for a transaction to be allowed into the
 	// mempool and relayed by scaling the base fee (which is the minimum
-	// free transaction relay fee).  minRelayTxFee is in Satoshi/KB, so
-	// divide the transaction size by 1000 to convert to kilobytes.  Also,
-	// integer division is used so fees only increase on full kilobyte
-	// boundaries.
-	minFee := (1 + serializedSize/1000) * int64(minRelayTxFee)
+	// free transaction relay fee). minTxRelayFee is in Satoshi/kB so
+	// multiply by serializedSize (which is in bytes) and divide by 1000 to get
+	// minimum Satoshis.
+	minFee := (serializedSize * int64(minRelayTxFee)) / 1000
+
+	if minFee == 0 && minRelayTxFee > 0 {
+		minFee = int64(minRelayTxFee)
+	}
 
 	// Set the minimum fee to the maximum possible value if the calculated
 	// fee is not in the valid range for monetary amounts.
diff --git a/policy_test.go b/policy_test.go
index 8ad0f79b..22c936e3 100644
--- a/policy_test.go
+++ b/policy_test.go
@@ -22,22 +22,24 @@ func TestCalcMinRequiredTxRelayFee(t *testing.T) {
 		want     int64          // Expected fee.
 	}{
 		{
-			"zero value with default minimum relay fee",
-			0,
-			defaultMinRelayTxFee,
-			int64(defaultMinRelayTxFee),
+			// Ensure combination of size and fee that are less than 1000
+			// produce a non-zero fee.
+			"250 bytes with relay fee of 3",
+			250,
+			3,
+			3,
 		},
 		{
 			"100 bytes with default minimum relay fee",
 			100,
 			defaultMinRelayTxFee,
-			int64(defaultMinRelayTxFee),
+			100,
 		},
 		{
 			"max standard tx size with default minimum relay fee",
 			maxStandardTxSize,
 			defaultMinRelayTxFee,
-			101000,
+			100000,
 		},
 		{
 			"max standard tx size with max satoshi relay fee",
@@ -45,6 +47,36 @@ func TestCalcMinRequiredTxRelayFee(t *testing.T) {
 			btcutil.MaxSatoshi,
 			btcutil.MaxSatoshi,
 		},
+		{
+			"1500 bytes with 5000 relay fee",
+			1500,
+			5000,
+			7500,
+		},
+		{
+			"1500 bytes with 3000 relay fee",
+			1500,
+			3000,
+			4500,
+		},
+		{
+			"782 bytes with 5000 relay fee",
+			782,
+			5000,
+			3910,
+		},
+		{
+			"782 bytes with 3000 relay fee",
+			782,
+			3000,
+			2346,
+		},
+		{
+			"782 bytes with 2550 relay fee",
+			782,
+			2550,
+			1994,
+		},
 	}
 
 	for _, test := range tests {