diff --git a/Cargo.toml b/Cargo.toml
index 1b6416f07d7..c7b25ff82b9 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -31,9 +31,6 @@ unindent = { version = "0.2.1", optional = true }
 # support crate for multiple-pymethods feature
 inventory = { version = "0.3.0", optional = true }
 
-# coroutine implementation
-futures-util = "0.3"
-
 # crate integrations that can be added using the eponymous features
 anyhow = { version = "1.0", optional = true }
 chrono = { version = "0.4.25", default-features = false, optional = true }
diff --git a/src/coroutine.rs b/src/coroutine.rs
index c4c7bbf29cd..050b0f5c741 100644
--- a/src/coroutine.rs
+++ b/src/coroutine.rs
@@ -1,7 +1,7 @@
 //! Python coroutine implementation, used notably when wrapping `async fn`
 //! with `#[pyfunction]`/`#[pymethods]`.
+use std::task::Waker;
 use std::{
-    any::Any,
     future::Future,
     panic,
     pin::Pin,
@@ -9,13 +9,11 @@ use std::{
     task::{Context, Poll},
 };
 
-use futures_util::FutureExt;
 use pyo3_macros::{pyclass, pymethods};
 
 use crate::{
     coroutine::waker::AsyncioWaker,
     exceptions::{PyAttributeError, PyRuntimeError, PyStopIteration},
-    panic::PanicException,
     pyclass::IterNextOutput,
     types::{PyIterator, PyString},
     IntoPy, Py, PyAny, PyErr, PyObject, PyResult, Python,
@@ -25,19 +23,18 @@ pub(crate) mod cancel;
 mod waker;
 
 use crate::coroutine::cancel::ThrowCallback;
+use crate::panic::PanicException;
 pub use cancel::CancelHandle;
 
 const COROUTINE_REUSED_ERROR: &str = "cannot reuse already awaited coroutine";
 
-type FutureOutput = Result<PyResult<PyObject>, Box<dyn Any + Send>>;
-
 /// Python coroutine wrapping a [`Future`].
 #[pyclass(crate = "crate")]
 pub struct Coroutine {
     name: Option<Py<PyString>>,
     qualname_prefix: Option<&'static str>,
     throw_callback: Option<ThrowCallback>,
-    future: Option<Pin<Box<dyn Future<Output = FutureOutput> + Send>>>,
+    future: Option<Pin<Box<dyn Future<Output = PyResult<PyObject>> + Send>>>,
     waker: Option<Arc<AsyncioWaker>>,
 }
 
@@ -68,7 +65,7 @@ impl Coroutine {
             name,
             qualname_prefix,
             throw_callback,
-            future: Some(Box::pin(panic::AssertUnwindSafe(wrap).catch_unwind())),
+            future: Some(Box::pin(wrap)),
             waker: None,
         }
     }
@@ -98,14 +95,20 @@ impl Coroutine {
         } else {
             self.waker = Some(Arc::new(AsyncioWaker::new()));
         }
-        let waker = futures_util::task::waker(self.waker.clone().unwrap());
+        let waker = Waker::from(self.waker.clone().unwrap());
         // poll the Rust future and forward its results if ready
-        if let Poll::Ready(res) = future_rs.as_mut().poll(&mut Context::from_waker(&waker)) {
-            self.close();
-            return match res {
-                Ok(res) => Ok(IterNextOutput::Return(res?)),
-                Err(err) => Err(PanicException::from_panic_payload(err)),
-            };
+        // polling is UnwindSafe because the future is dropped in case of panic
+        let poll = || future_rs.as_mut().poll(&mut Context::from_waker(&waker));
+        match panic::catch_unwind(panic::AssertUnwindSafe(poll)) {
+            Ok(Poll::Ready(res)) => {
+                self.close();
+                return Ok(IterNextOutput::Return(res?));
+            }
+            Err(err) => {
+                self.close();
+                return Err(PanicException::from_panic_payload(err));
+            }
+            _ => {}
         }
         // otherwise, initialize the waker `asyncio.Future`
         if let Some(future) = self.waker.as_ref().unwrap().initialize_future(py)? {
@@ -113,7 +116,7 @@ impl Coroutine {
             // and will yield itself if its result has not been set in polling above
             if let Some(future) = PyIterator::from_object(future).unwrap().next() {
                 // future has not been leaked into Python for now, and Rust code can only call
-                // `set_result(None)` in `ArcWake` implementation, so it's safe to unwrap
+                // `set_result(None)` in `Wake` implementation, so it's safe to unwrap
                 return Ok(IterNextOutput::Yield(future.unwrap().into()));
             }
         }
diff --git a/src/coroutine/waker.rs b/src/coroutine/waker.rs
index 7ed4103fbb7..8a1166ce3fb 100644
--- a/src/coroutine/waker.rs
+++ b/src/coroutine/waker.rs
@@ -1,11 +1,11 @@
 use crate::sync::GILOnceCell;
 use crate::types::PyCFunction;
 use crate::{intern, wrap_pyfunction, Py, PyAny, PyObject, PyResult, Python};
-use futures_util::task::ArcWake;
 use pyo3_macros::pyfunction;
 use std::sync::Arc;
+use std::task::Wake;
 
-/// Lazy `asyncio.Future` wrapper, implementing [`ArcWake`] by calling `Future.set_result`.
+/// Lazy `asyncio.Future` wrapper, implementing [`Wake`] by calling `Future.set_result`.
 ///
 /// asyncio future is let uninitialized until [`initialize_future`][1] is called.
 /// If [`wake`][2] is called before future initialization (during Rust future polling),
@@ -31,10 +31,14 @@ impl AsyncioWaker {
     }
 }
 
-impl ArcWake for AsyncioWaker {
-    fn wake_by_ref(arc_self: &Arc<Self>) {
+impl Wake for AsyncioWaker {
+    fn wake(self: Arc<Self>) {
+        self.wake_by_ref()
+    }
+
+    fn wake_by_ref(self: &Arc<Self>) {
         Python::with_gil(|gil| {
-            if let Some(loop_and_future) = arc_self.0.get_or_init(gil, || None) {
+            if let Some(loop_and_future) = self.0.get_or_init(gil, || None) {
                 loop_and_future
                     .set_result(gil)
                     .expect("unexpected error in coroutine waker");