diff --git a/src/coroutine.rs b/src/coroutine.rs
index 7dd73cbb..415bbc88 100644
--- a/src/coroutine.rs
+++ b/src/coroutine.rs
@@ -15,7 +15,7 @@ use crate::{
     exceptions::{PyAttributeError, PyRuntimeError, PyStopIteration},
     panic::PanicException,
     types::{PyIterator, PyString},
-    IntoPy, Py, PyAny, PyErr, PyObject, PyResult, Python,
+    IntoPy, Py, PyAny, PyErr, PyNativeType, PyObject, PyResult, Python,
 };
 
 pub(crate) mod cancel;
@@ -107,7 +107,10 @@ impl Coroutine {
         if let Some(future) = self.waker.as_ref().unwrap().initialize_future(py)? {
             // `asyncio.Future` must be awaited; fortunately, it implements `__iter__ = __await__`
             // and will yield itself if its result has not been set in polling above
-            if let Some(future) = PyIterator::from_object(future).unwrap().next() {
+            if let Some(future) = PyIterator::from_bound_object(&future.as_borrowed())
+                .unwrap()
+                .next()
+            {
                 // future has not been leaked into Python for now, and Rust code can only call
                 // `set_result(None)` in `Wake` implementation, so it's safe to unwrap
                 return Ok(future.unwrap().into());
diff --git a/src/types/any.rs b/src/types/any.rs
index 102099c5..7d5f226a 100644
--- a/src/types/any.rs
+++ b/src/types/any.rs
@@ -2126,7 +2126,7 @@ impl<'py> PyAnyMethods<'py> for Bound<'py, PyAny> {
     }
 
     fn iter(&self) -> PyResult<Bound<'py, PyIterator>> {
-        PyIterator::from_object2(self)
+        PyIterator::from_bound_object(self)
     }
 
     fn get_type(&self) -> &'py PyType {
diff --git a/src/types/frozenset.rs b/src/types/frozenset.rs
index 1bcdce4c..ff0be7b5 100644
--- a/src/types/frozenset.rs
+++ b/src/types/frozenset.rs
@@ -209,7 +209,7 @@ mod impl_ {
     impl<'py> BoundFrozenSetIterator<'py> {
         pub(super) fn new(frozenset: Bound<'py, PyFrozenSet>) -> Self {
             Self {
-                it: PyIterator::from_object2(&frozenset).unwrap(),
+                it: PyIterator::from_bound_object(&frozenset).unwrap(),
             }
         }
     }
diff --git a/src/types/iterator.rs b/src/types/iterator.rs
index 67866348..e2703286 100644
--- a/src/types/iterator.rs
+++ b/src/types/iterator.rs
@@ -31,14 +31,23 @@ pyobject_native_type_named!(PyIterator);
 pyobject_native_type_extract!(PyIterator);
 
 impl PyIterator {
-    /// Constructs a `PyIterator` from a Python iterable object.
-    ///
-    /// Equivalent to Python's built-in `iter` function.
+    /// Deprecated form of `PyIterator::from_bound_object`.
+    #[cfg_attr(
+        not(feature = "gil-refs"),
+        deprecated(
+            since = "0.21.0",
+            note = "`PyIterator::from_object` will be replaced by `PyIterator::from_bound_object` in a future PyO3 version"
+        )
+    )]
     pub fn from_object(obj: &PyAny) -> PyResult<&PyIterator> {
-        Self::from_object2(&obj.as_borrowed()).map(Bound::into_gil_ref)
+        Self::from_bound_object(&obj.as_borrowed()).map(Bound::into_gil_ref)
     }
 
-    pub(crate) fn from_object2<'py>(obj: &Bound<'py, PyAny>) -> PyResult<Bound<'py, PyIterator>> {
+    /// Builds an iterator for an iterable Python object; the equivalent of calling `iter(obj)` in Python.
+    ///
+    /// Usually it is more convenient to write [`obj.iter()`][crate::types::any::PyAnyMethods::iter],
+    /// which is a more concise way of calling this function.
+    pub fn from_bound_object<'py>(obj: &Bound<'py, PyAny>) -> PyResult<Bound<'py, PyIterator>> {
         unsafe {
             ffi::PyObject_GetIter(obj.as_ptr())
                 .assume_owned_or_err(obj.py())
@@ -135,6 +144,7 @@ impl<'v> crate::PyTryFrom<'v> for PyIterator {
 }
 
 #[cfg(test)]
+#[cfg_attr(not(feature = "gil-refs"), allow(deprecated))]
 mod tests {
     use super::PyIterator;
     use crate::exceptions::PyTypeError;
diff --git a/src/types/set.rs b/src/types/set.rs
index be65500b..d59a9e3f 100644
--- a/src/types/set.rs
+++ b/src/types/set.rs
@@ -289,7 +289,7 @@ mod impl_ {
     impl<'py> BoundSetIterator<'py> {
         pub(super) fn new(set: Bound<'py, PySet>) -> Self {
             Self {
-                it: PyIterator::from_object2(&set).unwrap(),
+                it: PyIterator::from_bound_object(&set).unwrap(),
             }
         }
     }