diff --git a/futures-core/src/task/spawn.rs b/futures-core/src/task/spawn.rs
index 895e81b598..eaa969096c 100644
--- a/futures-core/src/task/spawn.rs
+++ b/futures-core/src/task/spawn.rs
@@ -12,7 +12,7 @@ pub trait Spawn {
     /// represent relatively rare scenarios, such as the executor
     /// having been shut down so that it is no longer able to accept
     /// tasks.
-    fn spawn_obj(&mut self, future: FutureObj<'static, ()>)
+    fn spawn_obj(&self, future: FutureObj<'static, ()>)
         -> Result<(), SpawnError>;
 
     /// Determines whether the executor is able to spawn new tasks.
@@ -38,7 +38,7 @@ pub trait LocalSpawn {
     /// represent relatively rare scenarios, such as the executor
     /// having been shut down so that it is no longer able to accept
     /// tasks.
-    fn spawn_local_obj(&mut self, future: LocalFutureObj<'static, ()>)
+    fn spawn_local_obj(&self, future: LocalFutureObj<'static, ()>)
         -> Result<(), SpawnError>;
 
     /// Determines whether the executor is able to spawn new tasks.
@@ -87,8 +87,8 @@ impl SpawnError {
     }
 }
 
-impl<Sp: ?Sized + Spawn> Spawn for &mut Sp {
-    fn spawn_obj(&mut self, future: FutureObj<'static, ()>)
+impl<Sp: ?Sized + Spawn> Spawn for &Sp {
+    fn spawn_obj(&self, future: FutureObj<'static, ()>)
     -> Result<(), SpawnError> {
         Sp::spawn_obj(self, future)
     }
@@ -98,8 +98,8 @@ impl<Sp: ?Sized + Spawn> Spawn for &mut Sp {
     }
 }
 
-impl<Sp: ?Sized + LocalSpawn> LocalSpawn for &mut Sp {
-    fn spawn_local_obj(&mut self, future: LocalFutureObj<'static, ()>)
+impl<Sp: ?Sized + LocalSpawn> LocalSpawn for &Sp {
+    fn spawn_local_obj(&self, future: LocalFutureObj<'static, ()>)
     -> Result<(), SpawnError> {
         Sp::spawn_local_obj(self, future)
     }
@@ -115,7 +115,7 @@ mod if_alloc {
     use super::*;
 
     impl<Sp: ?Sized + Spawn> Spawn for Box<Sp> {
-        fn spawn_obj(&mut self, future: FutureObj<'static, ()>)
+        fn spawn_obj(&self, future: FutureObj<'static, ()>)
         -> Result<(), SpawnError> {
             (**self).spawn_obj(future)
         }
@@ -126,7 +126,7 @@ mod if_alloc {
     }
 
     impl<Sp: ?Sized + LocalSpawn> LocalSpawn for Box<Sp> {
-        fn spawn_local_obj(&mut self, future: LocalFutureObj<'static, ()>)
+        fn spawn_local_obj(&self, future: LocalFutureObj<'static, ()>)
         -> Result<(), SpawnError> {
             (**self).spawn_local_obj(future)
         }
diff --git a/futures-executor/src/local_pool.rs b/futures-executor/src/local_pool.rs
index 9985dca5b9..5142354b09 100644
--- a/futures-executor/src/local_pool.rs
+++ b/futures-executor/src/local_pool.rs
@@ -341,7 +341,7 @@ impl<S: Stream + Unpin> Iterator for BlockingStream<S> {
 
 impl Spawn for LocalSpawner {
     fn spawn_obj(
-        &mut self,
+        &self,
         future: FutureObj<'static, ()>,
     ) -> Result<(), SpawnError> {
         if let Some(incoming) = self.incoming.upgrade() {
@@ -363,7 +363,7 @@ impl Spawn for LocalSpawner {
 
 impl LocalSpawn for LocalSpawner {
     fn spawn_local_obj(
-        &mut self,
+        &self,
         future: LocalFutureObj<'static, ()>,
     ) -> Result<(), SpawnError> {
         if let Some(incoming) = self.incoming.upgrade() {
diff --git a/futures-executor/src/thread_pool.rs b/futures-executor/src/thread_pool.rs
index fded082f27..c06907ddc0 100644
--- a/futures-executor/src/thread_pool.rs
+++ b/futures-executor/src/thread_pool.rs
@@ -143,17 +143,7 @@ impl ThreadPool {
 
 impl Spawn for ThreadPool {
     fn spawn_obj(
-        &mut self,
-        future: FutureObj<'static, ()>,
-    ) -> Result<(), SpawnError> {
-        self.spawn_obj_ok(future);
-        Ok(())
-    }
-}
-
-impl Spawn for &ThreadPool {
-    fn spawn_obj(
-        &mut self,
+        &self,
         future: FutureObj<'static, ()>,
     ) -> Result<(), SpawnError> {
         self.spawn_obj_ok(future);
diff --git a/futures-executor/tests/local_pool.rs b/futures-executor/tests/local_pool.rs
index 44b0a76ff0..42fefcf172 100644
--- a/futures-executor/tests/local_pool.rs
+++ b/futures-executor/tests/local_pool.rs
@@ -39,7 +39,7 @@ fn run_until_single_future() {
 #[test]
 fn run_until_ignores_spawned() {
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
     spawn.spawn_local_obj(Box::pin(pending()).into()).unwrap();
     assert_eq!(pool.run_until(lazy(|_| ())), ());
 }
@@ -48,7 +48,7 @@ fn run_until_ignores_spawned() {
 fn run_until_executes_spawned() {
     let (tx, rx) = oneshot::channel();
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
     spawn.spawn_local_obj(Box::pin(lazy(move |_| {
         tx.send(()).unwrap();
         ()
@@ -69,8 +69,8 @@ fn run_executes_spawned() {
     let cnt2 = cnt.clone();
 
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
-    let mut spawn2 = pool.spawner();
+    let spawn = pool.spawner();
+    let spawn2 = pool.spawner();
 
     spawn.spawn_local_obj(Box::pin(lazy(move |_| {
         spawn2.spawn_local_obj(Box::pin(lazy(move |_| {
@@ -93,7 +93,7 @@ fn run_spawn_many() {
     let cnt = Rc::new(Cell::new(0));
 
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
 
     for _ in 0..ITER {
         let cnt = cnt.clone();
@@ -121,7 +121,7 @@ fn try_run_one_executes_one_ready() {
     let cnt = Rc::new(Cell::new(0));
 
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
 
     for _ in 0..ITER {
         spawn.spawn_local_obj(Box::pin(pending()).into()).unwrap();
@@ -150,7 +150,7 @@ fn try_run_one_returns_on_no_progress() {
     let cnt = Rc::new(Cell::new(0));
 
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
 
     let waker: Rc<Cell<Option<Waker>>> = Rc::new(Cell::new(None));
     {
@@ -189,7 +189,7 @@ fn run_until_stalled_returns_if_empty() {
 #[test]
 fn run_until_stalled_returns_multiple_times() {
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
     let cnt = Rc::new(Cell::new(0));
 
     let cnt1 = cnt.clone();
@@ -211,7 +211,7 @@ fn run_until_stalled_executes_all_ready() {
     let cnt = Rc::new(Cell::new(0));
 
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
 
     for i in 0..ITER {
         for _ in 0..PER_ITER {
@@ -236,7 +236,7 @@ fn run_until_stalled_executes_all_ready() {
 #[should_panic]
 fn nesting_run() {
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
 
     spawn.spawn_obj(Box::pin(lazy(|_| {
         let mut pool = LocalPool::new();
@@ -250,7 +250,7 @@ fn nesting_run() {
 #[should_panic]
 fn nesting_run_run_until_stalled() {
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
 
     spawn.spawn_obj(Box::pin(lazy(|_| {
         let mut pool = LocalPool::new();
@@ -297,7 +297,7 @@ fn tasks_are_scheduled_fairly() {
     }
 
     let mut pool = LocalPool::new();
-    let mut spawn = pool.spawner();
+    let spawn = pool.spawner();
 
     spawn.spawn_local_obj(Box::pin(Spin {
         state: state.clone(),
diff --git a/futures-test/src/task/noop_spawner.rs b/futures-test/src/task/noop_spawner.rs
index 947fd119e6..927a2e5cb0 100644
--- a/futures-test/src/task/noop_spawner.rs
+++ b/futures-test/src/task/noop_spawner.rs
@@ -27,7 +27,7 @@ impl NoopSpawner {
 
 impl Spawn for NoopSpawner {
     fn spawn_obj(
-        &mut self,
+        &self,
         _future: FutureObj<'static, ()>,
     ) -> Result<(), SpawnError> {
         Ok(())
diff --git a/futures-test/src/task/panic_spawner.rs b/futures-test/src/task/panic_spawner.rs
index 4206d44d9e..5fac9e9fd4 100644
--- a/futures-test/src/task/panic_spawner.rs
+++ b/futures-test/src/task/panic_spawner.rs
@@ -28,7 +28,7 @@ impl PanicSpawner {
 
 impl Spawn for PanicSpawner {
     fn spawn_obj(
-        &mut self,
+        &self,
         _future: FutureObj<'static, ()>,
     ) -> Result<(), SpawnError> {
         panic!("should not spawn")
diff --git a/futures-test/src/task/record_spawner.rs b/futures-test/src/task/record_spawner.rs
index 3b13d00222..b93bd472db 100644
--- a/futures-test/src/task/record_spawner.rs
+++ b/futures-test/src/task/record_spawner.rs
@@ -1,5 +1,6 @@
 use futures_core::future::FutureObj;
 use futures_core::task::{Spawn, SpawnError};
+use std::cell::{Ref, RefCell};
 
 /// An implementation of [`Spawn`](futures_core::task::Spawn) that records
 /// any [`Future`](futures_core::future::Future)s spawned on it.
@@ -14,37 +15,29 @@ use futures_core::task::{Spawn, SpawnError};
 /// recorder.spawn(async { }).unwrap();
 /// assert_eq!(recorder.spawned().len(), 1);
 /// ```
-#[derive(Debug)]
+#[derive(Debug, Default)]
 pub struct RecordSpawner {
-    spawned: Vec<FutureObj<'static, ()>>,
+    spawned: RefCell<Vec<FutureObj<'static, ()>>>,
 }
 
 impl RecordSpawner {
     /// Create a new instance
     pub fn new() -> Self {
-        Self {
-            spawned: Vec::new(),
-        }
+        Default::default()
     }
 
     /// Inspect any futures that were spawned onto this [`Spawn`].
-    pub fn spawned(&self) -> &[FutureObj<'static, ()>] {
-        &self.spawned
+    pub fn spawned(&self) -> Ref<'_, Vec<FutureObj<'static, ()>>> {
+        self.spawned.borrow()
     }
 }
 
 impl Spawn for RecordSpawner {
     fn spawn_obj(
-        &mut self,
+        &self,
         future: FutureObj<'static, ()>,
     ) -> Result<(), SpawnError> {
-        self.spawned.push(future);
+        self.spawned.borrow_mut().push(future);
         Ok(())
     }
 }
-
-impl Default for RecordSpawner {
-    fn default() -> Self {
-        Self::new()
-    }
-}
diff --git a/futures-util/src/compat/executor.rs b/futures-util/src/compat/executor.rs
index 1fe080055e..43b10c2553 100644
--- a/futures-util/src/compat/executor.rs
+++ b/futures-util/src/compat/executor.rs
@@ -68,7 +68,7 @@ where
     Ex: Executor01<Executor01Future> + Clone + Send + 'static,
 {
     fn spawn_obj(
-        &mut self,
+        &self,
         future: FutureObj<'static, ()>,
     ) -> Result<(), SpawnError03> {
         let future = future.unit_error().compat();
diff --git a/futures-util/src/stream/futures_unordered/mod.rs b/futures-util/src/stream/futures_unordered/mod.rs
index 6c8d8b1065..8cc15843a6 100644
--- a/futures-util/src/stream/futures_unordered/mod.rs
+++ b/futures-util/src/stream/futures_unordered/mod.rs
@@ -7,7 +7,7 @@ use crate::task::{AtomicWaker};
 use futures_core::future::{Future, FutureObj, LocalFutureObj};
 use futures_core::stream::{FusedStream, Stream};
 use futures_core::task::{Context, Poll, Spawn, LocalSpawn, SpawnError};
-use core::cell::UnsafeCell;
+use core::cell::{Cell, UnsafeCell};
 use core::fmt::{self, Debug};
 use core::iter::FromIterator;
 use core::marker::PhantomData;
@@ -61,8 +61,8 @@ const TERMINATED_SENTINEL_LENGTH: usize = usize::max_value();
 #[must_use = "streams do nothing unless polled"]
 pub struct FuturesUnordered<Fut> {
     ready_to_run_queue: Arc<ReadyToRunQueue<Fut>>,
-    len: usize,
-    head_all: *const Task<Fut>,
+    len: Cell<usize>,
+    head_all: Cell<*const Task<Fut>>,
 }
 
 unsafe impl<Fut: Send> Send for FuturesUnordered<Fut> {}
@@ -70,7 +70,7 @@ unsafe impl<Fut: Sync> Sync for FuturesUnordered<Fut> {}
 impl<Fut> Unpin for FuturesUnordered<Fut> {}
 
 impl Spawn for FuturesUnordered<FutureObj<'_, ()>> {
-    fn spawn_obj(&mut self, future_obj: FutureObj<'static, ()>)
+    fn spawn_obj(&self, future_obj: FutureObj<'static, ()>)
         -> Result<(), SpawnError>
     {
         self.push(future_obj);
@@ -79,7 +79,7 @@ impl Spawn for FuturesUnordered<FutureObj<'_, ()>> {
 }
 
 impl LocalSpawn for FuturesUnordered<LocalFutureObj<'_, ()>> {
-    fn spawn_local_obj(&mut self, future_obj: LocalFutureObj<'static, ()>)
+    fn spawn_local_obj(&self, future_obj: LocalFutureObj<'static, ()>)
         -> Result<(), SpawnError>
     {
         self.push(future_obj);
@@ -134,8 +134,8 @@ impl<Fut: Future> FuturesUnordered<Fut> {
         });
 
         FuturesUnordered {
-            len: 0,
-            head_all: ptr::null_mut(),
+            len: 0.into(),
+            head_all: Cell::from(ptr::null()),
             ready_to_run_queue,
         }
     }
@@ -152,12 +152,14 @@ impl<Fut> FuturesUnordered<Fut> {
     ///
     /// This represents the total number of in-flight futures.
     pub fn len(&self) -> usize {
-        if self.len == TERMINATED_SENTINEL_LENGTH { 0 } else { self.len }
+        let len = self.len.get();
+        if len == TERMINATED_SENTINEL_LENGTH { 0 } else { len }
     }
 
     /// Returns `true` if the set contains no futures.
     pub fn is_empty(&self) -> bool {
-        self.len == 0 || self.len == TERMINATED_SENTINEL_LENGTH
+        let len = self.len.get();
+        len == 0 || len == TERMINATED_SENTINEL_LENGTH
     }
 
     /// Push a future into the set.
@@ -166,7 +168,7 @@ impl<Fut> FuturesUnordered<Fut> {
     /// call [`poll`](core::future::Future::poll) on the submitted future. The caller must
     /// ensure that [`FuturesUnordered::poll_next`](Stream::poll_next) is called
     /// in order to receive wake-up notifications for the given future.
-    pub fn push(&mut self, future: Fut) {
+    pub fn push(&self, future: Fut) {
         let task = Arc::new(Task {
             future: UnsafeCell::new(Some(future)),
             next_all: UnsafeCell::new(ptr::null_mut()),
@@ -178,8 +180,8 @@ impl<Fut> FuturesUnordered<Fut> {
 
         // If we've previously marked ourselves as terminated we need to reset
         // len to 0 to track it correctly
-        if self.len == TERMINATED_SENTINEL_LENGTH {
-            self.len = 0;
+        if self.len.get() == TERMINATED_SENTINEL_LENGTH {
+            self.len.set(0);
         }
 
         // Right now our task has a strong reference count of 1. We transfer
@@ -202,7 +204,7 @@ impl<Fut> FuturesUnordered<Fut> {
     /// Returns an iterator that allows inspecting each future in the set.
     fn iter_pin_ref(self: Pin<&Self>) -> IterPinRef<'_, Fut> {
         IterPinRef {
-            task: self.head_all,
+            task: self.head_all.get(),
             len: self.len(),
             _marker: PhantomData,
         }
@@ -216,7 +218,7 @@ impl<Fut> FuturesUnordered<Fut> {
     /// Returns an iterator that allows modifying each future in the set.
     pub fn iter_pin_mut(self: Pin<&mut Self>) -> IterPinMut<'_, Fut> {
         IterPinMut {
-            task: self.head_all,
+            task: self.head_all.get(),
             len: self.len(),
             _marker: PhantomData
         }
@@ -263,17 +265,18 @@ impl<Fut> FuturesUnordered<Fut> {
     }
 
     /// Insert a new task into the internal linked list.
-    fn link(&mut self, task: Arc<Task<Fut>>) -> *const Task<Fut> {
+    fn link(&self, task: Arc<Task<Fut>>) -> *const Task<Fut> {
         let ptr = Arc::into_raw(task);
         unsafe {
-            *(*ptr).next_all.get() = self.head_all;
-            if !self.head_all.is_null() {
-                *(*self.head_all).prev_all.get() = ptr;
+            *(*ptr).next_all.get() = self.head_all.get();
+            if !self.head_all.get().is_null() {
+                *(*self.head_all.get()).prev_all.get() = ptr;
             }
         }
 
-        self.head_all = ptr;
-        self.len += 1;
+        self.head_all.set(ptr);
+        let old_len = self.len.get();
+        self.len.set(old_len + 1);
         ptr
     }
 
@@ -295,9 +298,10 @@ impl<Fut> FuturesUnordered<Fut> {
         if !prev.is_null() {
             *(*prev).next_all.get() = next;
         } else {
-            self.head_all = next;
+            self.head_all.set(next);
         }
-        self.len -= 1;
+        let old_len = self.len.get();
+        self.len.set(old_len - 1);
         task
     }
 }
@@ -319,7 +323,7 @@ impl<Fut: Future> Stream for FuturesUnordered<Fut> {
                     if self.is_empty() {
                         // We can only consider ourselves terminated once we
                         // have yielded a `None`
-                        self.len = TERMINATED_SENTINEL_LENGTH;
+                        self.len.set(TERMINATED_SENTINEL_LENGTH);
                         return Poll::Ready(None);
                     } else {
                         return Poll::Pending;
@@ -461,8 +465,8 @@ impl<Fut> Drop for FuturesUnordered<Fut> {
         // wakers flying around which contain `Task<Fut>` references
         // inside them. We'll let those naturally get deallocated.
         unsafe {
-            while !self.head_all.is_null() {
-                let head = self.head_all;
+            while !self.head_all.get().is_null() {
+                let head = self.head_all.get();
                 let task = self.unlink(head);
                 self.release_task(task);
             }
@@ -489,12 +493,12 @@ impl<Fut: Future> FromIterator<Fut> for FuturesUnordered<Fut> {
         I: IntoIterator<Item = Fut>,
     {
         let acc = FuturesUnordered::new();
-        iter.into_iter().fold(acc, |mut acc, item| { acc.push(item); acc })
+        iter.into_iter().fold(acc, |acc, item| { acc.push(item); acc })
     }
 }
 
 impl<Fut: Future> FusedStream for FuturesUnordered<Fut> {
     fn is_terminated(&self) -> bool {
-        self.len == TERMINATED_SENTINEL_LENGTH
+        self.len.get() == TERMINATED_SENTINEL_LENGTH
     }
 }
diff --git a/futures/tests/ready_queue.rs b/futures/tests/ready_queue.rs
index 8005800514..1fa7d79064 100644
--- a/futures/tests/ready_queue.rs
+++ b/futures/tests/ready_queue.rs
@@ -70,7 +70,7 @@ fn resolving_errors() {
 #[test]
 fn dropping_ready_queue() {
     block_on(future::lazy(move |_| {
-        let mut queue = FuturesUnordered::new();
+        let queue = FuturesUnordered::new();
         let (mut tx1, rx1) = oneshot::channel::<()>();
         let (mut tx2, rx2) = oneshot::channel::<()>();
         let (mut tx3, rx3) = oneshot::channel::<()>();