diff --git a/internal/mempool/v1/mempool_test.go b/internal/mempool/v1/mempool_test.go
index 09f431853..b338301b8 100644
--- a/internal/mempool/v1/mempool_test.go
+++ b/internal/mempool/v1/mempool_test.go
@@ -95,6 +95,18 @@ func setup(t testing.TB, cacheSize int, options ...TxMempoolOption) *TxMempool {
 	return NewTxMempool(log.TestingLogger().With("test", t.Name()), cfg.Mempool, appConnMem, 0, options...)
 }
 
+// mustCheckTx invokes txmp.CheckTx for the given transaction and waits until
+// its callback has finished executing. It fails t if CheckTx fails.
+func mustCheckTx(t *testing.T, txmp *TxMempool, spec string) {
+	done := make(chan struct{})
+	if err := txmp.CheckTx(context.Background(), []byte(spec), func(*abci.Response) {
+		close(done)
+	}, mempool.TxInfo{}); err != nil {
+		t.Fatalf("CheckTx for %q failed: %v", spec, err)
+	}
+	<-done
+}
+
 func checkTxs(t *testing.T, txmp *TxMempool, numTxs int, peerID uint16) []testTx {
 	txs := make([]testTx, numTxs)
 	txInfo := mempool.TxInfo{SenderID: peerID}
@@ -196,6 +208,76 @@ func TestTxMempool_Size(t *testing.T) {
 	require.Equal(t, int64(2850), txmp.SizeBytes())
 }
 
+func TestTxMempool_Eviction(t *testing.T) {
+	txmp := setup(t, 0)
+	txmp.config.Size = 5
+	txmp.config.MaxTxsBytes = 60
+	txExists := func(spec string) bool {
+		txmp.Lock()
+		defer txmp.Unlock()
+		key := types.Tx(spec).Key()
+		_, ok := txmp.txByKey[key]
+		return ok
+	}
+
+	// A transaction bigger than the mempool should be rejected even when there
+	// are slots available.
+	mustCheckTx(t, txmp, "big=0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef=1")
+	require.Equal(t, 0, txmp.Size())
+
+	// Nearly-fill the mempool with a low-priority transaction, to show that it
+	// is evicted even when slots are available for a higher-priority tx.
+	const bigTx = "big=0123456789abcdef0123456789abcdef0123456789abcdef01234=2"
+	mustCheckTx(t, txmp, bigTx)
+	require.Equal(t, 1, txmp.Size()) // bigTx is the only element
+	require.True(t, txExists(bigTx))
+	require.Equal(t, int64(len(bigTx)), txmp.SizeBytes())
+
+	// The next transaction should evict bigTx, because it is higher priority
+	// but does not fit on size.
+	mustCheckTx(t, txmp, "key1=0000=25")
+	require.True(t, txExists("key1=0000=25"))
+	require.False(t, txExists(bigTx))
+	require.Equal(t, int64(len("key1=0000=25")), txmp.SizeBytes())
+
+	// Now fill up the rest of the slots with other transactions.
+	mustCheckTx(t, txmp, "key2=0001=5")
+	mustCheckTx(t, txmp, "key3=0002=10")
+	mustCheckTx(t, txmp, "key4=0003=3")
+	mustCheckTx(t, txmp, "key5=0004=3")
+
+	// A new transaction with low priority should be discarded.
+	mustCheckTx(t, txmp, "key6=0005=1")
+	require.False(t, txExists("key6=0005=1"))
+
+	// A new transaction with higher priority should evict key5, which is the
+	// newest of the two transactions with lowest priority.
+	mustCheckTx(t, txmp, "key7=0006=7")
+	require.True(t, txExists("key7=0006=7"))  // new transaction added
+	require.False(t, txExists("key5=0004=3")) // newest low-priority tx evicted
+	require.True(t, txExists("key4=0003=3"))  // older low-priority tx retained
+
+	// Another new transaction evicts the other low-priority element.
+	mustCheckTx(t, txmp, "key8=0007=20")
+	require.True(t, txExists("key8=0007=20"))
+	require.False(t, txExists("key4=0003=3"))
+
+	// Now the lowest-priority tx is 5, so that should be the next to go.
+	mustCheckTx(t, txmp, "key9=0008=9")
+	require.True(t, txExists("key9=0008=9"))
+	require.False(t, txExists("k3y2=0001=5"))
+
+	// Add a transaction that requires eviction of multiple lower-priority
+	// entries, in order to fit the size of the element.
+	mustCheckTx(t, txmp, "key10=0123456789abcdef=11") // evict 10, 9, 7; keep 25, 20, 11
+	require.True(t, txExists("key1=0000=25"))
+	require.True(t, txExists("key8=0007=20"))
+	require.True(t, txExists("key10=0123456789abcdef=11"))
+	require.False(t, txExists("key3=0002=10"))
+	require.False(t, txExists("key9=0008=9"))
+	require.False(t, txExists("key7=0006=7"))
+}
+
 func TestTxMempool_Flush(t *testing.T) {
 	txmp := setup(t, 0)
 	txs := checkTxs(t, txmp, 100, 0)
@@ -438,6 +520,51 @@ func TestTxMempool_ConcurrentTxs(t *testing.T) {
 	require.Zero(t, txmp.SizeBytes())
 }
 
+func TestTxMempool_ExpiredTxs_Timestamp(t *testing.T) {
+	txmp := setup(t, 50)
+	txmp.config.TTLDuration = 5 * time.Millisecond
+
+	added1 := checkTxs(t, txmp, 25, 0)
+	require.Equal(t, len(added1), txmp.Size())
+
+	// Wait a while, then add some more transactions that should not be expired
+	// when the first batch TTLs out.
+	//
+	// ms: 0   1   2   3   4   5   6
+	//     ^           ^       ^   ^
+	//     |           |       |   +-- Update (triggers pruning)
+	//     |           |       +------ first batch expires
+	//     |           +-------------- second batch added
+	//     +-------------------------- first batch added
+	//
+	// The exact intervals are not important except that the delta should be
+	// large relative to the cost of CheckTx (ms vs. ns is fine here).
+	time.Sleep(3 * time.Millisecond)
+	added2 := checkTxs(t, txmp, 25, 1)
+
+	// Wait a while longer, so that the first batch will expire.
+	time.Sleep(3 * time.Millisecond)
+
+	// Trigger an update so that pruning will occur.
+	txmp.Lock()
+	defer txmp.Unlock()
+	require.NoError(t, txmp.Update(txmp.height+1, nil, nil, nil, nil))
+
+	// All the transactions in the original set should have been purged.
+	for _, tx := range added1 {
+		if _, ok := txmp.txByKey[tx.tx.Key()]; ok {
+			t.Errorf("Transaction %X should have been purged for TTL", tx.tx.Key())
+		}
+	}
+
+	// All the transactions added later should still be around.
+	for _, tx := range added2 {
+		if _, ok := txmp.txByKey[tx.tx.Key()]; !ok {
+			t.Errorf("Transaction %X should still be in the mempool, but is not", tx.tx.Key())
+		}
+	}
+}
+
 func TestTxMempool_ExpiredTxs_NumBlocks(t *testing.T) {
 	txmp := setup(t, 500)
 	txmp.height = 100