diff --git a/lite2/client.go b/lite2/client.go
index 61559a694..65040c133 100644
--- a/lite2/client.go
+++ b/lite2/client.go
@@ -703,13 +703,14 @@ func (c *Client) sequence(
 	newHeader *types.SignedHeader,
 	newVals *types.ValidatorSet,
 	now time.Time) error {
+
 	// 1) Verify any intermediate headers.
 	var (
 		interimHeader   *types.SignedHeader
 		interimNextVals *types.ValidatorSet
 		err             error
 	)
-	for height := trustedHeader.Height + 1; height < newHeader.Height; height++ {
+	for height := trustedHeader.Height + 1; height <= newHeader.Height; height++ {
 		interimHeader, err = c.signedHeaderFromPrimary(height)
 		if err != nil {
 			return errors.Wrapf(err, "failed to obtain the header #%d", height)
@@ -734,16 +735,17 @@ func (c *Client) sequence(
 			if err != nil {
 				return errors.Wrapf(err, "failed to obtain the vals #%d", height+1)
 			}
-		}
-		err = c.updateTrustedHeaderAndNextVals(interimHeader, interimNextVals)
-		if err != nil {
-			return errors.Wrapf(err, "failed to update trusted state #%d", height)
+			if !bytes.Equal(interimHeader.NextValidatorsHash, interimNextVals.Hash()) {
+				return errors.Errorf("expected next validator's hash %X, but got %X (height #%d)",
+					interimHeader.NextValidatorsHash,
+					interimNextVals.Hash(),
+					interimHeader.Height)
+			}
 		}
 		trustedHeader, trustedNextVals = interimHeader, interimNextVals
 	}
 
-	// 2) Verify the new header.
-	return VerifyAdjacent(c.chainID, c.latestTrustedHeader, newHeader, newVals, c.trustingPeriod, now)
+	return nil
 }
 
 // see VerifyHeader
@@ -757,7 +759,7 @@ func (c *Client) bisection(
 	interimVals := newVals
 	interimHeader := newHeader
 
-	for trustedHeader.Height < newHeader.Height {
+	for {
 		c.logger.Debug("Verify newHeader against trustedHeader",
 			"trustedHeight", trustedHeader.Height,
 			"trustedHash", hash2str(trustedHeader.Hash()),
@@ -767,24 +769,22 @@ func (c *Client) bisection(
 			c.trustLevel)
 		switch err.(type) {
 		case nil:
+			if interimHeader.Height == newHeader.Height {
+				return nil
+			}
+
 			// Update the lower bound to the previous upper bound
-			trustedHeader = interimHeader
-			trustedNextVals, err = c.validatorSetFromPrimary(interimHeader.Height + 1)
+			interimNextVals, err := c.validatorSetFromPrimary(interimHeader.Height + 1)
 			if err != nil {
 				return err
 			}
-			if !bytes.Equal(trustedHeader.NextValidatorsHash, trustedNextVals.Hash()) {
+			if !bytes.Equal(interimHeader.NextValidatorsHash, interimNextVals.Hash()) {
 				return errors.Errorf("expected next validator's hash %X, but got %X (height #%d)",
-					trustedHeader.NextValidatorsHash,
-					trustedNextVals.Hash(),
-					trustedHeader.Height)
-			}
-
-			err = c.updateTrustedHeaderAndNextVals(trustedHeader, trustedNextVals)
-			if err != nil {
-				return err
+					interimHeader.NextValidatorsHash,
+					interimNextVals.Hash(),
+					interimHeader.Height)
 			}
-
+			trustedHeader, trustedNextVals = interimHeader, interimNextVals
 			// Update the upper bound to the untrustedHeader
 			interimHeader, interimVals = newHeader, newVals
 
@@ -799,8 +799,6 @@ func (c *Client) bisection(
 			return errors.Wrapf(err, "failed to verify the header #%d", newHeader.Height)
 		}
 	}
-
-	return nil
 }
 
 // persist header and next validators to trustedStore.
@@ -841,6 +839,10 @@ func (c *Client) backwards(trustedHeader *types.SignedHeader, newHeader *types.S
 		err           error
 	)
 
+	if HeaderExpired(newHeader, c.trustingPeriod, now) {
+		return ErrOldHeaderExpired{newHeader.Time.Add(c.trustingPeriod), now}
+	}
+
 	for trustedHeader.Height > newHeader.Height {
 		interimHeader, err = c.signedHeaderFromPrimary(trustedHeader.Height - 1)
 		if err != nil {
@@ -857,10 +859,6 @@ func (c *Client) backwards(trustedHeader *types.SignedHeader, newHeader *types.S
 				trustedHeader.Time)
 		}
 
-		if HeaderExpired(interimHeader, c.trustingPeriod, now) {
-			return ErrOldHeaderExpired{interimHeader.Time.Add(c.trustingPeriod), now}
-		}
-
 		if !bytes.Equal(interimHeader.Hash(), trustedHeader.LastBlockID.Hash) {
 			return errors.Errorf("older header hash %X does not match trusted header's last block %X",
 				interimHeader.Hash(),
diff --git a/lite2/client_test.go b/lite2/client_test.go
index a6ffc31ab..a6b615227 100644
--- a/lite2/client_test.go
+++ b/lite2/client_test.go
@@ -57,6 +57,9 @@ var (
 )
 
 func TestClient_SequentialVerification(t *testing.T) {
+	newKeys := genPrivKeys(4)
+	newVals := newKeys.ToValidators(10, 1)
+
 	testCases := []struct {
 		name         string
 		otherHeaders map[int64]*types.SignedHeader // all except ^
@@ -138,6 +141,25 @@ func TestClient_SequentialVerification(t *testing.T) {
 			false,
 			true,
 		},
+		{
+			"bad: different validator set at height 3",
+			map[int64]*types.SignedHeader{
+				// trusted header
+				1: h1,
+				// interim header (3/3 signed)
+				2: h2,
+				// last header (3/3 signed)
+				3: h3,
+			},
+			map[int64]*types.ValidatorSet{
+				1: vals,
+				2: vals,
+				3: newVals,
+				4: newVals,
+			},
+			false,
+			true,
+		},
 	}
 
 	for _, tc := range testCases {
@@ -368,7 +390,8 @@ func TestClient_Cleanup(t *testing.T) {
 	require.NoError(t, err)
 
 	c.Stop()
-	c.Cleanup()
+	err = c.Cleanup()
+	require.NoError(t, err)
 
 	// Check no headers exist after Cleanup.
 	h, err := c.TrustedHeader(1, bTime.Add(1*time.Second))
@@ -747,9 +770,6 @@ func TestClient_BackwardsVerification(t *testing.T) {
 		Logger(log.TestingLogger()),
 	)
 	require.NoError(t, err)
-	err = c.Start()
-	require.NoError(t, err)
-	defer c.Stop()
 
 	// 1) header is missing => expect no error
 	h, err := c.VerifyHeaderAtHeight(2, bTime.Add(1*time.Hour).Add(1*time.Second))
@@ -762,6 +782,15 @@ func TestClient_BackwardsVerification(t *testing.T) {
 	h, err = c.VerifyHeaderAtHeight(1, bTime.Add(1*time.Hour).Add(1*time.Second))
 	assert.Error(t, err)
 	assert.NotNil(t, h)
+
+	// 3) already stored headers should return the header without error
+	h, err = c.VerifyHeaderAtHeight(3, bTime.Add(1*time.Hour).Add(1*time.Second))
+	assert.NoError(t, err)
+	assert.NotNil(t, h)
+
+	// 4) cannot verify a header in the future
+	_, err = c.VerifyHeaderAtHeight(4, bTime.Add(1*time.Hour).Add(1*time.Second))
+	assert.Error(t, err)
 }
 
 func TestClient_NewClientFromTrustedStore(t *testing.T) {