diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 8754286ee7d11..247786f08869e 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -260,6 +260,7 @@ I/O
 - Bug in :func:`read_excel` attempting to read chart sheets from .xlsx files (:issue:`41448`)
 - Bug in :func:`json_normalize` where ``errors=ignore`` could fail to ignore missing values of ``meta`` when ``record_path`` has a length greater than one (:issue:`41876`)
 - Bug in :func:`read_csv` with multi-header input and arguments referencing column names as tuples (:issue:`42446`)
+- Bug in :func:`Series.to_json` and :func:`DataFrame.to_json` where some attributes were skipped when serialising plain Python objects to JSON (:issue:`42768`, :issue:`33043`)
 -
 
 Period
diff --git a/pandas/_libs/src/ujson/python/objToJSON.c b/pandas/_libs/src/ujson/python/objToJSON.c
index cf530c8c07440..06c3d823f72d2 100644
--- a/pandas/_libs/src/ujson/python/objToJSON.c
+++ b/pandas/_libs/src/ujson/python/objToJSON.c
@@ -927,7 +927,6 @@ int Dir_iterNext(JSOBJ _obj, JSONTypeContext *tc) {
 
         GET_TC(tc)->itemName = itemName;
         GET_TC(tc)->itemValue = itemValue;
-        GET_TC(tc)->index++;
 
         itemName = attr;
         break;
diff --git a/pandas/tests/io/json/test_pandas.py b/pandas/tests/io/json/test_pandas.py
index d97ba8694818b..77a3394c08ef2 100644
--- a/pandas/tests/io/json/test_pandas.py
+++ b/pandas/tests/io/json/test_pandas.py
@@ -1769,3 +1769,18 @@ def test_to_json_multiindex_escape(self):
             "\"(Timestamp('2017-01-23 00:00:00'), 'bar')\":true}"
         )
         assert result == expected
+
+    def test_to_json_series_of_objects(self):
+        class _TestObject:
+            def __init__(self, a, b, _c, d):
+                self.a = a
+                self.b = b
+                self._c = _c
+                self.d = d
+
+            def e(self):
+                return 5
+
+        # JSON keys should be all non-callable non-underscore attributes, see GH-42768
+        series = Series([_TestObject(a=1, b=2, _c=3, d=4)])
+        assert json.loads(series.to_json()) == {"0": {"a": 1, "b": 2, "d": 4}}
diff --git a/pandas/tests/io/json/test_ujson.py b/pandas/tests/io/json/test_ujson.py
index 57a6b214cec84..58ccd31b7c940 100644
--- a/pandas/tests/io/json/test_ujson.py
+++ b/pandas/tests/io/json/test_ujson.py
@@ -720,6 +720,21 @@ def my_obj_handler(_):
             ujson.encode(obj_list, default_handler=str)
         )
 
+    def test_encode_object(self):
+        class _TestObject:
+            def __init__(self, a, b, _c, d):
+                self.a = a
+                self.b = b
+                self._c = _c
+                self.d = d
+
+            def e(self):
+                return 5
+
+        # JSON keys should be all non-callable non-underscore attributes, see GH-42768
+        test_object = _TestObject(a=1, b=2, _c=3, d=4)
+        assert ujson.decode(ujson.encode(test_object)) == {"a": 1, "b": 2, "d": 4}
+
 
 class TestNumpyJSONTests:
     @pytest.mark.parametrize("bool_input", [True, False])