diff --git a/x/auth/middleware/tx_priority.go b/x/auth/middleware/priority.go
similarity index 90%
rename from x/auth/middleware/tx_priority.go
rename to x/auth/middleware/priority.go
index 81d8d3124..fa6984b74 100644
--- a/x/auth/middleware/tx_priority.go
+++ b/x/auth/middleware/priority.go
@@ -50,12 +50,15 @@ func (h txPriorityHandler) SimulateTx(ctx context.Context, sdkTx sdk.Tx, req tx.
 	return h.next.SimulateTx(ctx, sdkTx, req)
 }
 
-// GetTxPriority returns a naive tx priority based on the total sum of all fees
+// GetTxPriority returns a naive tx priority based on the amount of the smallest denomination of the fee
 // provided in a transaction.
 func GetTxPriority(fee sdk.Coins) int64 {
 	var priority int64
 	for _, c := range fee {
-		priority += c.Amount.Int64()
+		p := c.Amount.Int64()
+		if priority == 0 || p < priority {
+			priority = p
+		}
 	}
 
 	return priority
diff --git a/x/auth/middleware/priority_test.go b/x/auth/middleware/priority_test.go
new file mode 100644
index 000000000..a06233f7e
--- /dev/null
+++ b/x/auth/middleware/priority_test.go
@@ -0,0 +1,38 @@
+package middleware_test
+
+import (
+	cryptotypes "github.com/cosmos/cosmos-sdk/crypto/types"
+	"github.com/cosmos/cosmos-sdk/testutil/testdata"
+	sdk "github.com/cosmos/cosmos-sdk/types"
+	"github.com/cosmos/cosmos-sdk/x/auth/middleware"
+	abci "github.com/tendermint/tendermint/abci/types"
+)
+
+func (s *MWTestSuite) TestPriority() {
+	ctx := s.SetupTest(true) // setup
+	txBuilder := s.clientCtx.TxConfig.NewTxBuilder()
+
+	txHandler := middleware.ComposeMiddlewares(noopTxHandler{}, middleware.TxPriorityHandler)
+
+	// keys and addresses
+	priv1, _, addr1 := testdata.KeyTestPubAddr()
+
+	// msg and signatures
+	msg := testdata.NewTestMsg(addr1)
+	atomCoin := sdk.NewCoin("atom", sdk.NewInt(150))
+	apeCoin := sdk.NewInt64Coin("ape", 1500000)
+	feeAmount := sdk.NewCoins(apeCoin, atomCoin)
+	gasLimit := testdata.NewTestGasLimit()
+	s.Require().NoError(txBuilder.SetMsgs(msg))
+	txBuilder.SetFeeAmount(feeAmount)
+	txBuilder.SetGasLimit(gasLimit)
+
+	privs, accNums, accSeqs := []cryptotypes.PrivKey{priv1}, []uint64{0}, []uint64{0}
+	tx, _, err := s.createTestTx(txBuilder, privs, accNums, accSeqs, ctx.ChainID())
+	s.Require().NoError(err)
+
+	// txHandler errors with insufficient fees
+	res, err := txHandler.CheckTx(sdk.WrapSDKContext(ctx), tx, abci.RequestCheckTx{})
+	s.Require().NoError(err, "Middleware should not have errored on too low fee for local gasPrice")
+	s.Require().Equal(atomCoin.Amount.Int64(), res.Priority, "priority should be atom amount")
+}