diff --git a/include/pybind11/pytypes.h b/include/pybind11/pytypes.h
index 7aafab6dc..027e36098 100644
--- a/include/pybind11/pytypes.h
+++ b/include/pybind11/pytypes.h
@@ -1470,11 +1470,17 @@ public:
     PYBIND11_OBJECT_DEFAULT(iterator, object, PyIter_Check)
 
     iterator &operator++() {
+        init();
         advance();
         return *this;
     }
 
     iterator operator++(int) {
+        // Note: We must call init() first so that rv.value is
+        // the same as this->value just before calling advance().
+        // Otherwise, dereferencing the returned iterator may call
+        // advance() again and return the 3rd item instead of the 1st.
+        init();
         auto rv = *this;
         advance();
         return rv;
@@ -1482,15 +1488,12 @@ public:
 
     // NOLINTNEXTLINE(readability-const-return-type) // PR #3263
     reference operator*() const {
-        if (m_ptr && !value.ptr()) {
-            auto &self = const_cast<iterator &>(*this);
-            self.advance();
-        }
+        init();
         return value;
     }
 
     pointer operator->() const {
-        operator*();
+        init();
         return &value;
     }
 
@@ -1513,6 +1516,13 @@ public:
     friend bool operator!=(const iterator &a, const iterator &b) { return a->ptr() != b->ptr(); }
 
 private:
+    void init() const {
+        if (m_ptr && !value.ptr()) {
+            auto &self = const_cast<iterator &>(*this);
+            self.advance();
+        }
+    }
+
     void advance() {
         value = reinterpret_steal<object>(PyIter_Next(m_ptr));
         if (value.ptr() == nullptr && PyErr_Occurred()) {
diff --git a/tests/test_pytypes.cpp b/tests/test_pytypes.cpp
index 19f65ce7e..8df4cdd3f 100644
--- a/tests/test_pytypes.cpp
+++ b/tests/test_pytypes.cpp
@@ -150,6 +150,18 @@ TEST_SUBMODULE(pytypes, m) {
     m.def("get_iterator", [] { return py::iterator(); });
     // test_iterable
     m.def("get_iterable", [] { return py::iterable(); });
+    m.def("get_first_item_from_iterable", [](const py::iterable &iter) {
+        // This tests the postfix increment operator
+        py::iterator it = iter.begin();
+        py::iterator it2 = it++;
+        return *it2;
+    });
+    m.def("get_second_item_from_iterable", [](const py::iterable &iter) {
+        // This tests the prefix increment operator
+        py::iterator it = iter.begin();
+        ++it;
+        return *it;
+    });
     m.def("get_frozenset_from_iterable",
           [](const py::iterable &iter) { return py::frozenset(iter); });
     m.def("get_list_from_iterable", [](const py::iterable &iter) { return py::list(iter); });
diff --git a/tests/test_pytypes.py b/tests/test_pytypes.py
index 39d0b619b..9fd24b34f 100644
--- a/tests/test_pytypes.py
+++ b/tests/test_pytypes.py
@@ -52,6 +52,11 @@ def test_from_iterable(pytype, from_iter_func):
 
 def test_iterable(doc):
     assert doc(m.get_iterable) == "get_iterable() -> Iterable"
+    lins = [1, 2, 3]
+    i = m.get_first_item_from_iterable(lins)
+    assert i == 1
+    i = m.get_second_item_from_iterable(lins)
+    assert i == 2
 
 
 def test_float(doc):