diff --git a/futures-util/src/stream/select_with_strategy.rs b/futures-util/src/stream/select_with_strategy.rs
index 6ccb321aaf..97417d3858 100644
--- a/futures-util/src/stream/select_with_strategy.rs
+++ b/futures-util/src/stream/select_with_strategy.rs
@@ -1,5 +1,4 @@
 use super::assert_stream;
-use crate::stream::{Fuse, StreamExt};
 use core::{fmt, pin::Pin};
 use futures_core::stream::{FusedStream, Stream};
 use futures_core::task::{Context, Poll};
@@ -14,6 +13,13 @@ pub enum PollNext {
     Right,
 }
 
+enum PollSide {
+    /// Poll the first stream.
+    Left,
+    /// Poll the second stream.
+    Right,
+}
+
 impl PollNext {
     /// Toggle the value and return the old one.
     #[must_use]
@@ -35,14 +41,40 @@ impl Default for PollNext {
     }
 }
 
+enum InternalState {
+    Start,
+    LeftFinished,
+    RightFinished,
+    BothFinished,
+}
+
+impl InternalState {
+    fn finish(&mut self, ps: PollSide) {
+        match (&self, ps) {
+            (InternalState::Start, PollSide::Left) => {
+                *self = InternalState::LeftFinished;
+            }
+            (InternalState::Start, PollSide::Right) => {
+                *self = InternalState::RightFinished;
+            }
+            (InternalState::LeftFinished, PollSide::Right)
+            | (InternalState::RightFinished, PollSide::Left) => {
+                *self = InternalState::BothFinished;
+            }
+            _ => {}
+        }
+    }
+}
+
 pin_project! {
     /// Stream for the [`select_with_strategy()`] function. See function docs for details.
     #[must_use = "streams do nothing unless polled"]
     pub struct SelectWithStrategy<St1, St2, Clos, State> {
         #[pin]
-        stream1: Fuse<St1>,
+        stream1: St1,
         #[pin]
-        stream2: Fuse<St2>,
+        stream2: St2,
+        internal_state: InternalState,
         state: State,
         clos: Clos,
     }
@@ -121,9 +153,10 @@ where
     State: Default,
 {
     assert_stream::<St1::Item, _>(SelectWithStrategy {
-        stream1: stream1.fuse(),
-        stream2: stream2.fuse(),
+        stream1,
+        stream2,
         state: Default::default(),
+        internal_state: InternalState::Start,
         clos: which,
     })
 }
@@ -132,7 +165,7 @@ impl<St1, St2, Clos, State> SelectWithStrategy<St1, St2, Clos, State> {
     /// Acquires a reference to the underlying streams that this combinator is
     /// pulling from.
     pub fn get_ref(&self) -> (&St1, &St2) {
-        (self.stream1.get_ref(), self.stream2.get_ref())
+        (&self.stream1, &self.stream2)
     }
 
     /// Acquires a mutable reference to the underlying streams that this
@@ -141,7 +174,7 @@ impl<St1, St2, Clos, State> SelectWithStrategy<St1, St2, Clos, State> {
     /// Note that care must be taken to avoid tampering with the state of the
     /// stream which may otherwise confuse this combinator.
     pub fn get_mut(&mut self) -> (&mut St1, &mut St2) {
-        (self.stream1.get_mut(), self.stream2.get_mut())
+        (&mut self.stream1, &mut self.stream2)
     }
 
     /// Acquires a pinned mutable reference to the underlying streams that this
@@ -151,7 +184,7 @@ impl<St1, St2, Clos, State> SelectWithStrategy<St1, St2, Clos, State> {
     /// stream which may otherwise confuse this combinator.
     pub fn get_pin_mut(self: Pin<&mut Self>) -> (Pin<&mut St1>, Pin<&mut St2>) {
         let this = self.project();
-        (this.stream1.get_pin_mut(), this.stream2.get_pin_mut())
+        (this.stream1, this.stream2)
     }
 
     /// Consumes this combinator, returning the underlying streams.
@@ -159,7 +192,7 @@ impl<St1, St2, Clos, State> SelectWithStrategy<St1, St2, Clos, State> {
     /// Note that this may discard intermediate state of this combinator, so
     /// care should be taken to avoid losing resources when this is called.
     pub fn into_inner(self) -> (St1, St2) {
-        (self.stream1.into_inner(), self.stream2.into_inner())
+        (self.stream1, self.stream2)
     }
 }
 
@@ -170,7 +203,10 @@ where
     Clos: FnMut(&mut State) -> PollNext,
 {
     fn is_terminated(&self) -> bool {
-        self.stream1.is_terminated() && self.stream2.is_terminated()
+        match self.internal_state {
+            InternalState::BothFinished => true,
+            _ => false,
+        }
     }
 }
 
@@ -185,35 +221,60 @@ where
     fn poll_next(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Option<St1::Item>> {
         let this = self.project();
 
-        match (this.clos)(this.state) {
-            PollNext::Left => poll_inner(this.stream1, this.stream2, cx),
-            PollNext::Right => poll_inner(this.stream2, this.stream1, cx),
+        match this.internal_state {
+            InternalState::Start => match (this.clos)(this.state) {
+                PollNext::Left => {
+                    match this.stream1.poll_next(cx) {
+                        Poll::Ready(Some(item)) => return Poll::Ready(Some(item)),
+                        Poll::Ready(None) => {
+                            this.internal_state.finish(PollSide::Left);
+                        }
+                        Poll::Pending => (),
+                    };
+                    match this.stream2.poll_next(cx) {
+                        Poll::Ready(None) => {
+                            this.internal_state.finish(PollSide::Right);
+                            Poll::Ready(None)
+                        }
+                        a => a,
+                    }
+                }
+                PollNext::Right => {
+                    match this.stream2.poll_next(cx) {
+                        Poll::Ready(Some(item)) => return Poll::Ready(Some(item)),
+                        Poll::Ready(None) => {
+                            this.internal_state.finish(PollSide::Right);
+                        }
+                        Poll::Pending => (),
+                    };
+                    match this.stream1.poll_next(cx) {
+                        Poll::Ready(None) => {
+                            this.internal_state.finish(PollSide::Left);
+                            Poll::Ready(None)
+                        }
+                        a => a,
+                    }
+                }
+            },
+            InternalState::LeftFinished => match this.stream2.poll_next(cx) {
+                Poll::Ready(None) => {
+                    *this.internal_state = InternalState::BothFinished;
+                    Poll::Ready(None)
+                }
+                a => a,
+            },
+            InternalState::RightFinished => match this.stream1.poll_next(cx) {
+                Poll::Ready(None) => {
+                    *this.internal_state = InternalState::BothFinished;
+                    Poll::Ready(None)
+                }
+                a => a,
+            },
+            InternalState::BothFinished => Poll::Ready(None),
         }
     }
 }
 
-fn poll_inner<St1, St2>(
-    a: Pin<&mut St1>,
-    b: Pin<&mut St2>,
-    cx: &mut Context<'_>,
-) -> Poll<Option<St1::Item>>
-where
-    St1: Stream,
-    St2: Stream<Item = St1::Item>,
-{
-    let a_done = match a.poll_next(cx) {
-        Poll::Ready(Some(item)) => return Poll::Ready(Some(item)),
-        Poll::Ready(None) => true,
-        Poll::Pending => false,
-    };
-
-    match b.poll_next(cx) {
-        Poll::Ready(Some(item)) => Poll::Ready(Some(item)),
-        Poll::Ready(None) if a_done => Poll::Ready(None),
-        Poll::Ready(None) | Poll::Pending => Poll::Pending,
-    }
-}
-
 impl<St1, St2, Clos, State> fmt::Debug for SelectWithStrategy<St1, St2, Clos, State>
 where
     St1: fmt::Debug,