diff --git a/electrum/blockchain.py b/electrum/blockchain.py
index f911d4b1e..43564e353 100644
--- a/electrum/blockchain.py
+++ b/electrum/blockchain.py
@@ -37,7 +37,9 @@ from .logging import get_logger, Logger
 _logger = get_logger(__name__)
 
 HEADER_SIZE = 80  # bytes
-MAX_TARGET = 0x00000000FFFF0000000000000000000000000000000000000000000000000000
+
+# see https://github.com/bitcoin/bitcoin/blob/feedb9c84e72e4fff489810a2bbeec09bcda5763/src/chainparams.cpp#L76
+MAX_TARGET = 0x00000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff  # compact: 0x1d00ffff
 
 
 class MissingHeader(Exception):
@@ -540,20 +542,37 @@ class Blockchain(Logger):
 
     @classmethod
     def bits_to_target(cls, bits: int) -> int:
+        # arith_uint256::SetCompact in Bitcoin Core
+        if not (0 <= bits < (1 << 32)):
+            raise Exception(f"bits should be uint32. got {bits!r}")
         bitsN = (bits >> 24) & 0xff
-        if not (0x03 <= bitsN <= 0x1d):
-            raise Exception("First part of bits should be in [0x03, 0x1d]")
-        bitsBase = bits & 0xffffff
-        if not (0x8000 <= bitsBase <= 0x7fffff):
-            raise Exception("Second part of bits should be in [0x8000, 0x7fffff]")
-        return bitsBase << (8 * (bitsN-3))
+        bitsBase = bits & 0x7fffff
+        if bitsN <= 3:
+            target = bitsBase >> (8 * (3-bitsN))
+        else:
+            target = bitsBase << (8 * (bitsN-3))
+        if target != 0 and bits & 0x800000 != 0:
+            # Bit number 24 (0x800000) represents the sign of N
+            raise Exception("target cannot be negative")
+        if (target != 0 and
+                (bitsN > 34 or
+                 (bitsN > 33 and bitsBase > 0xff) or
+                 (bitsN > 32 and bitsBase > 0xffff))):
+            raise Exception("target has overflown")
+        return target
 
     @classmethod
     def target_to_bits(cls, target: int) -> int:
-        c = ("%064x" % target)[2:]
-        while c[:2] == '00' and len(c) > 6:
-            c = c[2:]
-        bitsN, bitsBase = len(c) // 2, int.from_bytes(bfh(c[:6]), byteorder='big')
+        # arith_uint256::GetCompact in Bitcoin Core
+        # see https://github.com/bitcoin/bitcoin/blob/7fcf53f7b4524572d1d0c9a5fdc388e87eb02416/src/arith_uint256.cpp#L223
+        c = target.to_bytes(length=32, byteorder='big')
+        bitsN = len(c)
+        while bitsN > 0 and c[0] == 0:
+            c = c[1:]
+            bitsN -= 1
+            if len(c) < 3:
+                c += b'\x00'
+        bitsBase = int.from_bytes(c[:3], byteorder='big')
         if bitsBase >= 0x800000:
             bitsN += 1
             bitsBase >>= 8
diff --git a/electrum/tests/test_blockchain.py b/electrum/tests/test_blockchain.py
index 17d0d836f..a58c688fe 100644
--- a/electrum/tests/test_blockchain.py
+++ b/electrum/tests/test_blockchain.py
@@ -384,6 +384,47 @@ class TestBlockchain(ElectrumTestCase):
         self.assertEqual([chain_u], self.get_chains_that_contain_header_helper(self.HEADERS['O']))
         self.assertEqual([chain_z, chain_l], self.get_chains_that_contain_header_helper(self.HEADERS['I']))
 
+    def test_target_to_bits(self):
+        # https://github.com/bitcoin/bitcoin/blob/7fcf53f7b4524572d1d0c9a5fdc388e87eb02416/src/arith_uint256.h#L269
+        self.assertEqual(0x05123456, Blockchain.target_to_bits(0x1234560000))
+        self.assertEqual(0x0600c0de, Blockchain.target_to_bits(0xc0de000000))
+
+        # tests from https://github.com/bitcoin/bitcoin/blob/a7d17daa5cd8bf6398d5f8d7e77290009407d6ea/src/test/arith_uint256_tests.cpp#L411
+        tuples = (
+            (0, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x00123456, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x01003456, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x02000056, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x03000000, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x04000000, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x00923456, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x01803456, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x02800056, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x03800000, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x04800000, 0x0000000000000000000000000000000000000000000000000000000000000000, 0),
+            (0x01123456, 0x0000000000000000000000000000000000000000000000000000000000000012, 0x01120000),
+            (0x02123456, 0x0000000000000000000000000000000000000000000000000000000000001234, 0x02123400),
+            (0x03123456, 0x0000000000000000000000000000000000000000000000000000000000123456, 0x03123456),
+            (0x04123456, 0x0000000000000000000000000000000000000000000000000000000012345600, 0x04123456),
+            (0x05009234, 0x0000000000000000000000000000000000000000000000000000000092340000, 0x05009234),
+            (0x20123456, 0x1234560000000000000000000000000000000000000000000000000000000000, 0x20123456),
+        )
+        for nbits1, target, nbits2 in tuples:
+            with self.subTest(original_compact_nbits=nbits1.to_bytes(length=4, byteorder="big").hex()):
+                num = Blockchain.bits_to_target(nbits1)
+                self.assertEqual(target, num)
+                self.assertEqual(nbits2, Blockchain.target_to_bits(num))
+
+        # Make sure that we don't generate compacts with the 0x00800000 bit set
+        self.assertEqual(0x02008000, Blockchain.target_to_bits(0x80))
+
+        with self.assertRaises(Exception):  # target cannot be negative
+            Blockchain.bits_to_target(0x01fedcba)
+        with self.assertRaises(Exception):  # target cannot be negative
+            Blockchain.bits_to_target(0x04923456)
+        with self.assertRaises(Exception):  # overflow
+            Blockchain.bits_to_target(0xff123456)
+
 
 class TestVerifyHeader(ElectrumTestCase):