diff --git a/bson/__init__.py b/bson/__init__.py
index d0a8daa27..fd11c9952 100644
--- a/bson/__init__.py
+++ b/bson/__init__.py
@@ -896,12 +896,21 @@ def _name_value_to_bson(
     in_fallback_call: bool = False,
 ) -> bytes:
     """Encode a single name, value pair."""
+
+    was_integer_overflow = False
+
     # First see if the type is already cached. KeyError will only ever
     # happen once per subtype.
     try:
         return _ENCODERS[type(value)](name, value, check_keys, opts)  # type: ignore
     except KeyError:
         pass
+    except OverflowError:
+        if not isinstance(value, int):
+            raise
+
+        # Give the fallback_encoder a chance
+        was_integer_overflow = True
 
     # Second, fall back to trying _type_marker. This has to be done
     # before the loop below since users could subclass one of our
@@ -927,7 +936,7 @@ def _name_value_to_bson(
     # is done after trying the custom type encoder because checking for each
     # subtype is expensive.
     for base in _BUILT_IN_TYPES:
-        if isinstance(value, base):
+        if not was_integer_overflow and isinstance(value, base):
             func = _ENCODERS[base]
             # Cache this type for faster subsequent lookup.
             _ENCODERS[type(value)] = func
@@ -941,6 +950,8 @@ def _name_value_to_bson(
             name, fallback_encoder(value), check_keys, opts, in_fallback_call=True
         )
 
+    if was_integer_overflow:
+        raise OverflowError("BSON can only handle up to 8-byte ints")
     raise InvalidDocument(f"cannot encode object: {value!r}, of type: {type(value)!r}")
 
 
diff --git a/bson/_cbsonmodule.c b/bson/_cbsonmodule.c
index 5918a678c..68ea6b63c 100644
--- a/bson/_cbsonmodule.c
+++ b/bson/_cbsonmodule.c
@@ -662,6 +662,13 @@ static int write_element_to_buffer(PyObject* self, buffer_t buffer,
 
 static void
 _set_cannot_encode(PyObject* value) {
+    if (PyLong_Check(value)) {
+        if ((PyLong_AsLongLong(value) == -1) && PyErr_Occurred()) {
+            return PyErr_SetString(PyExc_OverflowError,
+                    "MongoDB can only handle up to 8-byte ints");
+        }
+    }
+
     PyObject* type = NULL;
     PyObject* InvalidDocument = _error("InvalidDocument");
     if (InvalidDocument == NULL) {
@@ -1069,16 +1076,17 @@ static int _write_element_to_buffer(PyObject* self, buffer_t buffer,
             long long long_long_value;
             PyErr_Clear();
             long_long_value = PyLong_AsLongLong(value);
-            if (PyErr_Occurred()) { /* Overflow AGAIN */
-                PyErr_SetString(PyExc_OverflowError,
-                                "MongoDB can only handle up to 8-byte ints");
-                return 0;
+            if (PyErr_Occurred()) {
+                /* Ignore error and give the fallback_encoder a chance. */
+                PyErr_Clear();
+            } else {
+                *(pymongo_buffer_get_buffer(buffer) + type_byte) = 0x12;
+                return buffer_write_int64(buffer, (int64_t)long_long_value);
             }
-            *(pymongo_buffer_get_buffer(buffer) + type_byte) = 0x12;
-            return buffer_write_int64(buffer, (int64_t)long_long_value);
+        } else {
+            *(pymongo_buffer_get_buffer(buffer) + type_byte) = 0x10;
+            return buffer_write_int32(buffer, (int32_t)int_value);
         }
-        *(pymongo_buffer_get_buffer(buffer) + type_byte) = 0x10;
-        return buffer_write_int32(buffer, (int32_t)int_value);
     } else if (PyFloat_Check(value)) {
         const double d = PyFloat_AsDouble(value);
         *(pymongo_buffer_get_buffer(buffer) + type_byte) = 0x01;
diff --git a/doc/contributors.rst b/doc/contributors.rst
index e6d5e5310..2a4ca1ea4 100644
--- a/doc/contributors.rst
+++ b/doc/contributors.rst
@@ -97,3 +97,4 @@ The following is a list of people who have contributed to
 - Sean Cheah (thalassemia)
 - Dainis Gorbunovs (DainisGorbunovs)
 - Iris Ho (sleepyStick)
+- Stephan Hof (stephan-hof)
diff --git a/test/test_custom_types.py b/test/test_custom_types.py
index 14d7b4b05..7e190483a 100644
--- a/test/test_custom_types.py
+++ b/test/test_custom_types.py
@@ -274,6 +274,22 @@ class TestBSONFallbackEncoder(unittest.TestCase):
         with self.assertRaises(TypeError):
             encode(document, codec_options=codecopts)
 
+    def test_call_only_once_for_not_handled_big_integers(self):
+        called_with = []
+
+        def fallback_encoder(value):
+            called_with.append(value)
+            return value
+
+        codecopts = self._get_codec_options(fallback_encoder)
+        document = {"a": {"b": {"c": 2 << 65}}}
+
+        msg = "MongoDB can only handle up to 8-byte ints"
+        with self.assertRaises(OverflowError, msg=msg):
+            encode(document, codec_options=codecopts)
+
+        self.assertEqual(called_with, [2 << 65])
+
 
 class TestBSONTypeEnDeCodecs(unittest.TestCase):
     def test_instantiation(self):
@@ -623,6 +639,15 @@ class TestCollectionWCustomType(IntegrationTest):
     def tearDown(self):
         self.db.test.drop()
 
+    def test_overflow_int_w_custom_decoder(self):
+        type_registry = TypeRegistry(fallback_encoder=lambda val: str(val))
+        codec_options = CodecOptions(type_registry=type_registry)
+        collection = self.db.get_collection("test", codec_options=codec_options)
+
+        collection.insert_one({"_id": 1, "data": 2**520})
+        ret = collection.find_one()
+        self.assertEqual(ret["data"], str(2**520))
+
     def test_command_errors_w_custom_type_decoder(self):
         db = self.db
         test_doc = {"_id": 1, "data": "a"}