diff --git a/pkg/core/mempool/mem_pool.go b/pkg/core/mempool/mem_pool.go
index 9a99a1774..e0371fe2a 100644
--- a/pkg/core/mempool/mem_pool.go
+++ b/pkg/core/mempool/mem_pool.go
@@ -46,6 +46,8 @@ type Pool struct {
 	lock         sync.RWMutex
 	verifiedMap  map[util.Uint256]*item
 	verifiedTxes items
+	inputs       []*transaction.Input
+	claims       []*transaction.Input
 
 	capacity int
 }
@@ -127,6 +129,35 @@ func (mp *Pool) containsKey(hash util.Uint256) bool {
 	return false
 }
 
+// findIndexForInput finds an index in a sorted Input pointers slice that is
+// appropriate to place this input into (or which contains an identical Input).
+func findIndexForInput(slice []*transaction.Input, input *transaction.Input) int {
+	return sort.Search(len(slice), func(n int) bool {
+		return input.Cmp(slice[n]) <= 0
+	})
+}
+
+// pushInputToSortedSlice pushes new Input into the given slice.
+func pushInputToSortedSlice(slice *[]*transaction.Input, input *transaction.Input) {
+	n := findIndexForInput(*slice, input)
+	*slice = append(*slice, input)
+	if n != len(*slice)-1 {
+		copy((*slice)[n+1:], (*slice)[n:])
+		(*slice)[n] = input
+	}
+}
+
+// dropInputFromSortedSlice removes given input from the given slice.
+func dropInputFromSortedSlice(slice *[]*transaction.Input, input *transaction.Input) {
+	n := findIndexForInput(*slice, input)
+	if n == len(*slice) || *input != *(*slice)[n] {
+		// Not present.
+		return
+	}
+	copy((*slice)[n:], (*slice)[n+1:])
+	*slice = (*slice)[:len(*slice)-1]
+}
+
 // Add tries to add given transaction to the Pool.
 func (mp *Pool) Add(t *transaction.Transaction, fee Feer) error {
 	var pItem = &item{
@@ -175,6 +206,19 @@ func (mp *Pool) Add(t *transaction.Transaction, fee Feer) error {
 		copy(mp.verifiedTxes[n+1:], mp.verifiedTxes[n:])
 		mp.verifiedTxes[n] = pItem
 	}
+
+	// For lots of inputs it might be easier to push them all and sort
+	// afterwards, but that requires benchmarking.
+	for i := range t.Inputs {
+		pushInputToSortedSlice(&mp.inputs, &t.Inputs[i])
+	}
+	if t.Type == transaction.ClaimType {
+		claim := t.Data.(*transaction.ClaimTX)
+		for i := range claim.Claims {
+			pushInputToSortedSlice(&mp.claims, &claim.Claims[i])
+		}
+	}
+
 	updateMempoolMetrics(len(mp.verifiedTxes))
 	mp.lock.Unlock()
 	return nil
@@ -184,10 +228,10 @@ func (mp *Pool) Add(t *transaction.Transaction, fee Feer) error {
 // nothing if it doesn't).
 func (mp *Pool) Remove(hash util.Uint256) {
 	mp.lock.Lock()
-	if _, ok := mp.verifiedMap[hash]; ok {
+	if it, ok := mp.verifiedMap[hash]; ok {
 		var num int
 		delete(mp.verifiedMap, hash)
-		for num := range mp.verifiedTxes {
+		for num = range mp.verifiedTxes {
 			if hash.Equals(mp.verifiedTxes[num].txn.Hash()) {
 				break
 			}
@@ -197,6 +241,15 @@ func (mp *Pool) Remove(hash util.Uint256) {
 		} else if num == len(mp.verifiedTxes)-1 {
 			mp.verifiedTxes = mp.verifiedTxes[:num]
 		}
+		for i := range it.txn.Inputs {
+			dropInputFromSortedSlice(&mp.inputs, &it.txn.Inputs[i])
+		}
+		if it.txn.Type == transaction.ClaimType {
+			claim := it.txn.Data.(*transaction.ClaimTX)
+			for i := range claim.Claims {
+				dropInputFromSortedSlice(&mp.claims, &claim.Claims[i])
+			}
+		}
 	}
 	updateMempoolMetrics(len(mp.verifiedTxes))
 	mp.lock.Unlock()
@@ -210,14 +263,33 @@ func (mp *Pool) RemoveStale(isOK func(*transaction.Transaction) bool) {
 	// We expect a lot of changes, so it's easier to allocate a new slice
 	// rather than move things in an old one.
 	newVerifiedTxes := make([]*item, 0, mp.capacity)
+	newInputs := mp.inputs[:0]
+	newClaims := mp.claims[:0]
 	for _, itm := range mp.verifiedTxes {
 		if isOK(itm.txn) {
 			newVerifiedTxes = append(newVerifiedTxes, itm)
+			for i := range itm.txn.Inputs {
+				newInputs = append(newInputs, &itm.txn.Inputs[i])
+			}
+			if itm.txn.Type == transaction.ClaimType {
+				claim := itm.txn.Data.(*transaction.ClaimTX)
+				for i := range claim.Claims {
+					newClaims = append(newClaims, &claim.Claims[i])
+				}
+			}
 		} else {
 			delete(mp.verifiedMap, itm.txn.Hash())
 		}
 	}
+	sort.Slice(newInputs, func(i, j int) bool {
+		return newInputs[i].Cmp(newInputs[j]) < 0
+	})
+	sort.Slice(newClaims, func(i, j int) bool {
+		return newClaims[i].Cmp(newClaims[j]) < 0
+	})
 	mp.verifiedTxes = newVerifiedTxes
+	mp.inputs = newInputs
+	mp.claims = newClaims
 	mp.lock.Unlock()
 }
 
@@ -259,16 +331,18 @@ func (mp *Pool) GetVerifiedTransactions() []TxWithFee {
 
 // verifyInputs is an internal unprotected version of Verify.
 func (mp *Pool) verifyInputs(tx *transaction.Transaction) bool {
-	if len(tx.Inputs) == 0 {
-		return true
+	for i := range tx.Inputs {
+		n := findIndexForInput(mp.inputs, &tx.Inputs[i])
+		if n < len(mp.inputs) && *mp.inputs[n] == tx.Inputs[i] {
+			return false
+		}
 	}
-	for num := range mp.verifiedTxes {
-		txn := mp.verifiedTxes[num].txn
-		for i := range txn.Inputs {
-			for j := 0; j < len(tx.Inputs); j++ {
-				if txn.Inputs[i] == tx.Inputs[j] {
-					return false
-				}
+	if tx.Type == transaction.ClaimType {
+		claim := tx.Data.(*transaction.ClaimTX)
+		for i := range claim.Claims {
+			n := findIndexForInput(mp.claims, &claim.Claims[i])
+			if n < len(mp.claims) && *mp.claims[n] == claim.Claims[i] {
+				return false
 			}
 		}
 	}
diff --git a/pkg/core/mempool/mem_pool_test.go b/pkg/core/mempool/mem_pool_test.go
index b6a9401be..6c1e1fe79 100644
--- a/pkg/core/mempool/mem_pool_test.go
+++ b/pkg/core/mempool/mem_pool_test.go
@@ -60,7 +60,73 @@ func TestMemPoolAddRemove(t *testing.T) {
 	t.Run("high priority", func(t *testing.T) { testMemPoolAddRemoveWithFeer(t, fs) })
 }
 
-func TestMemPoolVerify(t *testing.T) {
+func TestMemPoolAddRemoveWithInputsAndClaims(t *testing.T) {
+	mp := NewMemPool(50)
+	hash1, err := util.Uint256DecodeStringBE("a83ba6ede918a501558d3170a124324aedc89909e64c4ff2c6f863094f980b25")
+	require.NoError(t, err)
+	hash2, err := util.Uint256DecodeStringBE("629397158f852e838077bb2715b13a2e29b0a51c2157e5466321b70ed7904ce9")
+	require.NoError(t, err)
+	mpLessInputs := func(i, j int) bool {
+		return mp.inputs[i].Cmp(mp.inputs[j]) < 0
+	}
+	mpLessClaims := func(i, j int) bool {
+		return mp.claims[i].Cmp(mp.claims[j]) < 0
+	}
+
+	txm1 := newMinerTX(1)
+	txc1, claim1 := newClaimTX()
+	for i := 0; i < 5; i++ {
+		txm1.Inputs = append(txm1.Inputs, transaction.Input{PrevHash: hash1, PrevIndex: uint16(100 - i)})
+		claim1.Claims = append(claim1.Claims, transaction.Input{PrevHash: hash1, PrevIndex: uint16(100 - i)})
+	}
+	require.NoError(t, mp.Add(txm1, &FeerStub{}))
+	require.NoError(t, mp.Add(txc1, &FeerStub{}))
+	// Look inside.
+	assert.Equal(t, len(txm1.Inputs), len(mp.inputs))
+	assert.True(t, sort.SliceIsSorted(mp.inputs, mpLessInputs))
+	assert.Equal(t, len(claim1.Claims), len(mp.claims))
+	assert.True(t, sort.SliceIsSorted(mp.claims, mpLessClaims))
+
+	txm2 := newMinerTX(1)
+	txc2, claim2 := newClaimTX()
+	for i := 0; i < 10; i++ {
+		txm2.Inputs = append(txm2.Inputs, transaction.Input{PrevHash: hash2, PrevIndex: uint16(i)})
+		claim2.Claims = append(claim2.Claims, transaction.Input{PrevHash: hash2, PrevIndex: uint16(i)})
+	}
+	require.NoError(t, mp.Add(txm2, &FeerStub{}))
+	require.NoError(t, mp.Add(txc2, &FeerStub{}))
+	assert.Equal(t, len(txm1.Inputs)+len(txm2.Inputs), len(mp.inputs))
+	assert.True(t, sort.SliceIsSorted(mp.inputs, mpLessInputs))
+	assert.Equal(t, len(claim1.Claims)+len(claim2.Claims), len(mp.claims))
+	assert.True(t, sort.SliceIsSorted(mp.claims, mpLessClaims))
+
+	mp.Remove(txm1.Hash())
+	mp.Remove(txc2.Hash())
+	assert.Equal(t, len(txm2.Inputs), len(mp.inputs))
+	assert.True(t, sort.SliceIsSorted(mp.inputs, mpLessInputs))
+	assert.Equal(t, len(claim1.Claims), len(mp.claims))
+	assert.True(t, sort.SliceIsSorted(mp.claims, mpLessClaims))
+
+	require.NoError(t, mp.Add(txm1, &FeerStub{}))
+	require.NoError(t, mp.Add(txc2, &FeerStub{}))
+	assert.Equal(t, len(txm1.Inputs)+len(txm2.Inputs), len(mp.inputs))
+	assert.True(t, sort.SliceIsSorted(mp.inputs, mpLessInputs))
+	assert.Equal(t, len(claim1.Claims)+len(claim2.Claims), len(mp.claims))
+	assert.True(t, sort.SliceIsSorted(mp.claims, mpLessClaims))
+
+	mp.RemoveStale(func(t *transaction.Transaction) bool {
+		if t.Hash() == txc1.Hash() || t.Hash() == txm2.Hash() {
+			return false
+		}
+		return true
+	})
+	assert.Equal(t, len(txm1.Inputs), len(mp.inputs))
+	assert.True(t, sort.SliceIsSorted(mp.inputs, mpLessInputs))
+	assert.Equal(t, len(claim2.Claims), len(mp.claims))
+	assert.True(t, sort.SliceIsSorted(mp.claims, mpLessClaims))
+}
+
+func TestMemPoolVerifyInputs(t *testing.T) {
 	mp := NewMemPool(10)
 	tx := newMinerTX(1)
 	inhash1 := random.Uint256()
@@ -84,6 +150,33 @@ func TestMemPoolVerify(t *testing.T) {
 	require.Error(t, mp.Add(tx3, &FeerStub{}))
 }
 
+func TestMemPoolVerifyClaims(t *testing.T) {
+	mp := NewMemPool(50)
+	tx1, claim1 := newClaimTX()
+	hash1, err := util.Uint256DecodeStringBE("a83ba6ede918a501558d3170a124324aedc89909e64c4ff2c6f863094f980b25")
+	require.NoError(t, err)
+	hash2, err := util.Uint256DecodeStringBE("629397158f852e838077bb2715b13a2e29b0a51c2157e5466321b70ed7904ce9")
+	require.NoError(t, err)
+	for i := 0; i < 10; i++ {
+		claim1.Claims = append(claim1.Claims, transaction.Input{PrevHash: hash1, PrevIndex: uint16(i)})
+		claim1.Claims = append(claim1.Claims, transaction.Input{PrevHash: hash2, PrevIndex: uint16(i)})
+	}
+	require.Equal(t, true, mp.Verify(tx1))
+	require.NoError(t, mp.Add(tx1, &FeerStub{}))
+
+	tx2, claim2 := newClaimTX()
+	for i := 0; i < 10; i++ {
+		claim2.Claims = append(claim2.Claims, transaction.Input{PrevHash: hash2, PrevIndex: uint16(i + 10)})
+	}
+	require.Equal(t, true, mp.Verify(tx2))
+	require.NoError(t, mp.Add(tx2, &FeerStub{}))
+
+	tx3, claim3 := newClaimTX()
+	claim3.Claims = append(claim3.Claims, transaction.Input{PrevHash: hash1, PrevIndex: 0})
+	require.Equal(t, false, mp.Verify(tx3))
+	require.Error(t, mp.Add(tx3, &FeerStub{}))
+}
+
 func newMinerTX(i uint32) *transaction.Transaction {
 	return &transaction.Transaction{
 		Type: transaction.MinerType,
@@ -91,6 +184,14 @@ func newMinerTX(i uint32) *transaction.Transaction {
 	}
 }
 
+func newClaimTX() (*transaction.Transaction, *transaction.ClaimTX) {
+	cl := &transaction.ClaimTX{}
+	return &transaction.Transaction{
+		Type: transaction.ClaimType,
+		Data: cl,
+	}, cl
+}
+
 func TestOverCapacity(t *testing.T) {
 	var fs = &FeerStub{lowPriority: true}
 	const mempoolSize = 10
diff --git a/pkg/core/transaction/input.go b/pkg/core/transaction/input.go
index 3b7758ba3..c5b150c25 100644
--- a/pkg/core/transaction/input.go
+++ b/pkg/core/transaction/input.go
@@ -28,6 +28,16 @@ func (in *Input) EncodeBinary(bw *io.BinWriter) {
 	bw.WriteU16LE(in.PrevIndex)
 }
 
+// Cmp compares two Inputs by their hash and index allowing to make a set of
+// transactions ordered.
+func (in *Input) Cmp(other *Input) int {
+	hashcmp := in.PrevHash.CompareTo(other.PrevHash)
+	if hashcmp == 0 {
+		return int(in.PrevIndex) - int(other.PrevIndex)
+	}
+	return hashcmp
+}
+
 // MapInputsToSorted maps given slice of inputs into a new slice of pointers
 // to inputs sorted by their PrevHash and PrevIndex.
 func MapInputsToSorted(ins []Input) []*Input {
@@ -36,11 +46,7 @@ func MapInputsToSorted(ins []Input) []*Input {
 		ptrs[i] = &ins[i]
 	}
 	sort.Slice(ptrs, func(i, j int) bool {
-		hashcmp := ptrs[i].PrevHash.CompareTo(ptrs[j].PrevHash)
-		if hashcmp == 0 {
-			return ptrs[i].PrevIndex < ptrs[j].PrevIndex
-		}
-		return hashcmp < 0
+		return ptrs[i].Cmp(ptrs[j]) < 0
 	})
 	return ptrs
 }