diff --git a/electrum/ecc.py b/electrum/ecc.py
index 5ec9625a8..a8faeaf81 100644
--- a/electrum/ecc.py
+++ b/electrum/ecc.py
@@ -173,19 +173,34 @@ class ECPubkey(object):
         return ECPubkey._from_libsecp256k1_pubkey_ptr(pubkey)
 
     @classmethod
-    def from_signature65(cls, sig: bytes, msg_hash: bytes) -> Tuple['ECPubkey', bool]:
+    def from_signature65(cls, sig: bytes, msg_hash: bytes) -> Tuple['ECPubkey', bool, Optional[str]]:
         if len(sig) != 65:
             raise Exception(f'wrong encoding used for signature? len={len(sig)} (should be 65)')
         nV = sig[0]
-        if not (27 <= nV <= 34):
+        # as per BIP-0137:
+        #     27-30: p2pkh (uncompressed)
+        #     31-34: p2pkh (compressed)
+        #     35-38: p2wpkh-p2sh
+        #     39-42: p2wpkh
+        # However, the signatures we create do not respect this, and we instead always use 27-34,
+        # only distinguishing between compressed/uncompressed, so we treat those values as "any".
+        if not (27 <= nV <= 42):
             raise Exception("Bad encoding")
-        if nV >= 31:
-            compressed = True
+        txin_type_guess = None
+        compressed = True
+        if nV >= 39:
+            nV -= 12
+            txin_type_guess = "p2wpkh"
+        elif nV >= 35:
+            nV -= 8
+            txin_type_guess = "p2wpkh-p2sh"
+        elif nV >= 31:
             nV -= 4
         else:
             compressed = False
         recid = nV - 27
-        return cls.from_sig_string(sig[1:], recid, msg_hash), compressed
+        pubkey = cls.from_sig_string(sig[1:], recid, msg_hash)
+        return pubkey, compressed, txin_type_guess
 
     @classmethod
     def from_x_and_y(cls, x: int, y: int) -> 'ECPubkey':
@@ -294,7 +309,7 @@ class ECPubkey(object):
         assert_bytes(message)
         h = algo(message)
         try:
-            public_key, compressed = self.from_signature65(sig65, h)
+            public_key, compressed, txin_type_guess = self.from_signature65(sig65, h)
         except Exception:
             return False
         # check public key
@@ -376,12 +391,13 @@ def verify_message_with_address(address: str, sig65: bytes, message: bytes, *, n
     if net is None: net = constants.net
     h = sha256d(msg_magic(message))
     try:
-        public_key, compressed = ECPubkey.from_signature65(sig65, h)
+        public_key, compressed, txin_type_guess = ECPubkey.from_signature65(sig65, h)
     except Exception as e:
         return False
     # check public key using the address
     pubkey_hex = public_key.get_public_key_hex(compressed)
-    for txin_type in ['p2pkh','p2wpkh','p2wpkh-p2sh']:
+    txin_types = (txin_type_guess,) if txin_type_guess else ('p2pkh', 'p2wpkh', 'p2wpkh-p2sh')
+    for txin_type in txin_types:
         addr = pubkey_to_address(txin_type, pubkey_hex, net=net)
         if address == addr:
             break
diff --git a/electrum/plugins/digitalbitbox/digitalbitbox.py b/electrum/plugins/digitalbitbox/digitalbitbox.py
index f9c03e311..e745d08d7 100644
--- a/electrum/plugins/digitalbitbox/digitalbitbox.py
+++ b/electrum/plugins/digitalbitbox/digitalbitbox.py
@@ -491,7 +491,7 @@ class DigitalBitbox_KeyStore(Hardware_KeyStore):
                 sig_string = binascii.unhexlify(reply['sign'][0]['sig'])
                 recid = int(reply['sign'][0]['recid'], 16)
                 sig = ecc.construct_sig65(sig_string, recid, True)
-                pubkey, compressed = ecc.ECPubkey.from_signature65(sig, msg_hash)
+                pubkey, compressed, txin_type_guess = ecc.ECPubkey.from_signature65(sig, msg_hash)
                 addr = public_key_to_p2pkh(pubkey.get_public_key_bytes(compressed=compressed))
                 if ecc.verify_message_with_address(addr, sig, message) is False:
                     raise Exception(_("Could not sign message"))
diff --git a/electrum/tests/test_bitcoin.py b/electrum/tests/test_bitcoin.py
index f89239c89..3dd85b2df 100644
--- a/electrum/tests/test_bitcoin.py
+++ b/electrum/tests/test_bitcoin.py
@@ -225,6 +225,25 @@ class Test_bitcoin(ElectrumTestCase):
         self.assertTrue(ecc.verify_message_with_address(addr2, sig2, msg))
         self.assertFalse(ecc.verify_message_with_address(addr2, sig2, b'heyheyhey'))
 
+    def test_signmessage_segwit_witness_v0_address_test_we_also_accept_sigs_from_trezor(self):
+        """Trezor and some other projects use a slightly different scheme for message-signing
+        with p2wpkh and p2wpkh-p2sh addresses. Test that we also accept signatures from them.
+        see #3861
+        tests from https://github.com/trezor/trezor-firmware/blob/2ce1e6ba7dbe5bbaeeb336fff0a038e59cb40ef8/tests/device_tests/bitcoin/test_signmessage.py#L39
+        """
+        msg = b"This is an example of a signed message."
+        addr1 = "3L6TyTisPBmrDAj6RoKmDzNnj4eQi54gD2"
+        addr2 = "bc1qannfxke2tfd4l7vhepehpvt05y83v3qsf6nfkk"
+        sig1 = bytes.fromhex("23744de4516fac5c140808015664516a32fead94de89775cec7e24dbc24fe133075ac09301c4cc8e197bea4b6481661d5b8e9bf19d8b7b8a382ecdb53c2ee0750d")
+        sig2 = bytes.fromhex("28b55d7600d9e9a7e2a49155ddf3cfdb8e796c207faab833010fa41fb7828889bc47cf62348a7aaa0923c0832a589fab541e8f12eb54fb711c90e2307f0f66b194")
+        self.assertTrue(ecc.verify_message_with_address(address=addr1, sig65=sig1, message=msg))
+        self.assertTrue(ecc.verify_message_with_address(address=addr2, sig65=sig2, message=msg))
+        # if there is type information in the header of the sig (first byte), enforce that:
+        sig1_wrongtype = bytes.fromhex("27744de4516fac5c140808015664516a32fead94de89775cec7e24dbc24fe133075ac09301c4cc8e197bea4b6481661d5b8e9bf19d8b7b8a382ecdb53c2ee0750d")
+        sig2_wrongtype = bytes.fromhex("24b55d7600d9e9a7e2a49155ddf3cfdb8e796c207faab833010fa41fb7828889bc47cf62348a7aaa0923c0832a589fab541e8f12eb54fb711c90e2307f0f66b194")
+        self.assertFalse(ecc.verify_message_with_address(address=addr1, sig65=sig1_wrongtype, message=msg))
+        self.assertFalse(ecc.verify_message_with_address(address=addr2, sig65=sig2_wrongtype, message=msg))
+
     @needs_test_with_all_aes_implementations
     def test_decrypt_message(self):
         key = WalletStorage.get_eckey_from_password('pw123')