diff --git a/qa/rpc-tests/fundrawtransaction.py b/qa/rpc-tests/fundrawtransaction.py
index 998f822af..228574e67 100755
--- a/qa/rpc-tests/fundrawtransaction.py
+++ b/qa/rpc-tests/fundrawtransaction.py
@@ -58,7 +58,6 @@ class RawTransactionsTest(BitcoinTestFramework):
         self.nodes[0].sendtoaddress(self.nodes[2].getnewaddress(), 1.0)
         self.nodes[0].sendtoaddress(self.nodes[2].getnewaddress(), 5.0)
 
-        self.sync_all()
         self.nodes[0].generate(1)
         self.sync_all()
 
@@ -552,7 +551,6 @@ class RawTransactionsTest(BitcoinTestFramework):
         self.nodes[1].walletpassphrase("test", 100)
         signedTx = self.nodes[1].signrawtransaction(fundedTx['hex'])
         txId = self.nodes[1].sendrawtransaction(signedTx['hex'])
-        self.sync_all()
         self.nodes[1].generate(1)
         self.sync_all()
 
@@ -572,7 +570,6 @@ class RawTransactionsTest(BitcoinTestFramework):
 
         for i in range(0,20):
             self.nodes[0].sendtoaddress(self.nodes[1].getnewaddress(), 0.01)
-        self.sync_all()
         self.nodes[0].generate(1)
         self.sync_all()
 
@@ -603,7 +600,6 @@ class RawTransactionsTest(BitcoinTestFramework):
 
         for i in range(0,20):
             self.nodes[0].sendtoaddress(self.nodes[1].getnewaddress(), 0.01)
-        self.sync_all()
         self.nodes[0].generate(1)
         self.sync_all()
 
@@ -677,6 +673,15 @@ class RawTransactionsTest(BitcoinTestFramework):
         signedtx = self.nodes[0].signrawtransaction(signedtx["hex"])
         assert(signedtx["complete"])
         self.nodes[0].sendrawtransaction(signedtx["hex"])
+        self.nodes[0].generate(1)
+        self.sync_all()
+
+        #######################
+        # Test feeRate option #
+        #######################
+
+        # Make sure there is exactly one input so coin selection can't skew the result
+        assert_equal(len(self.nodes[3].listunspent(1)), 1)
 
         inputs = []
         outputs = {self.nodes[2].getnewaddress() : 1}
@@ -684,8 +689,9 @@ class RawTransactionsTest(BitcoinTestFramework):
         result = self.nodes[3].fundrawtransaction(rawtx) # uses min_relay_tx_fee (set by settxfee)
         result2 = self.nodes[3].fundrawtransaction(rawtx, {"feeRate": 2*min_relay_tx_fee})
         result3 = self.nodes[3].fundrawtransaction(rawtx, {"feeRate": 10*min_relay_tx_fee})
-        assert_equal(result['fee']*2, result2['fee'])
-        assert_equal(result['fee']*10, result3['fee'])
+        result_fee_rate = result['fee'] * 1000 / count_bytes(result['hex'])
+        assert_fee_amount(result2['fee'], count_bytes(result2['hex']), 2 * result_fee_rate)
+        assert_fee_amount(result3['fee'], count_bytes(result3['hex']), 10 * result_fee_rate)
 
 if __name__ == '__main__':
     RawTransactionsTest().main()
diff --git a/qa/rpc-tests/test_framework/util.py b/qa/rpc-tests/test_framework/util.py
index fc66ef287..782df52d6 100644
--- a/qa/rpc-tests/test_framework/util.py
+++ b/qa/rpc-tests/test_framework/util.py
@@ -477,6 +477,15 @@ def random_transaction(nodes, amount, min_fee, fee_increment, fee_variants):
 
     return (txid, signresult["hex"], fee)
 
+def assert_fee_amount(fee, tx_size, fee_per_kB):
+    """Assert the fee was in range"""
+    target_fee = tx_size * fee_per_kB / 1000
+    if fee < target_fee:
+        raise AssertionError("Fee of %s BTC too low! (Should be %s BTC)"%(str(fee), str(target_fee)))
+    # allow the wallet's estimation to be at most 2 bytes off
+    if fee > (tx_size + 2) * fee_per_kB / 1000:
+        raise AssertionError("Fee of %s BTC too high! (Should be %s BTC)"%(str(fee), str(target_fee)))
+
 def assert_equal(thing1, thing2):
     if thing1 != thing2:
         raise AssertionError("%s != %s"%(str(thing1),str(thing2)))
diff --git a/qa/rpc-tests/wallet.py b/qa/rpc-tests/wallet.py
index 9dda712f4..0b7eb52f0 100755
--- a/qa/rpc-tests/wallet.py
+++ b/qa/rpc-tests/wallet.py
@@ -11,12 +11,7 @@ class WalletTest (BitcoinTestFramework):
     def check_fee_amount(self, curr_balance, balance_with_fee, fee_per_byte, tx_size):
         """Return curr_balance after asserting the fee was in range"""
         fee = balance_with_fee - curr_balance
-        target_fee = fee_per_byte * tx_size
-        if fee < target_fee:
-            raise AssertionError("Fee of %s BTC too low! (Should be %s BTC)"%(str(fee), str(target_fee)))
-        # allow the node's estimation to be at most 2 bytes off
-        if fee > fee_per_byte * (tx_size + 2):
-            raise AssertionError("Fee of %s BTC too high! (Should be %s BTC)"%(str(fee), str(target_fee)))
+        assert_fee_amount(fee, tx_size, fee_per_byte * 1000)
         return curr_balance
 
     def __init__(self):