diff --git a/src/stream/stream/flat_map.rs b/src/stream/stream/flat_map.rs
index e07893a..d0cc73d 100644
--- a/src/stream/stream/flat_map.rs
+++ b/src/stream/stream/flat_map.rs
@@ -50,14 +50,15 @@ where
         let mut this = self.project();
         loop {
             if let Some(inner) = this.inner_stream.as_mut().as_pin_mut() {
-                if let item @ Some(_) = futures_core::ready!(inner.poll_next(cx)) {
-                    return Poll::Ready(item);
+                match futures_core::ready!(inner.poll_next(cx)) {
+                    item @ Some(_) => return Poll::Ready(item),
+                    None => this.inner_stream.set(None),
                 }
             }
 
             match futures_core::ready!(this.stream.as_mut().poll_next(cx)) {
+                inner @ Some(_) => this.inner_stream.set(inner.map(IntoStream::into_stream)),
                 None => return Poll::Ready(None),
-                Some(inner) => this.inner_stream.set(Some(inner.into_stream())),
             }
         }
     }
diff --git a/src/stream/stream/flatten.rs b/src/stream/stream/flatten.rs
index f2e275c..e7a498d 100644
--- a/src/stream/stream/flatten.rs
+++ b/src/stream/stream/flatten.rs
@@ -52,14 +52,15 @@ where
         let mut this = self.project();
         loop {
             if let Some(inner) = this.inner_stream.as_mut().as_pin_mut() {
-                if let item @ Some(_) = futures_core::ready!(inner.poll_next(cx)) {
-                    return Poll::Ready(item);
+                match futures_core::ready!(inner.poll_next(cx)) {
+                    item @ Some(_) => return Poll::Ready(item),
+                    None => this.inner_stream.set(None),
                 }
             }
 
             match futures_core::ready!(this.stream.as_mut().poll_next(cx)) {
+                inner @ Some(_) => this.inner_stream.set(inner.map(IntoStream::into_stream)),
                 None => return Poll::Ready(None),
-                Some(inner) => this.inner_stream.set(Some(inner.into_stream())),
             }
         }
     }
diff --git a/tests/stream.rs b/tests/stream.rs
index 3576cb9..3a19233 100644
--- a/tests/stream.rs
+++ b/tests/stream.rs
@@ -1,3 +1,5 @@
+use std::convert::identity;
+use std::marker::Unpin;
 use std::pin::Pin;
 use std::task::{Context, Poll};
 
@@ -108,3 +110,74 @@ fn merge_works_with_unfused_streams() {
         assert_eq!(xs, vec![92, 92]);
     });
 }
+
+struct S<T>(T);
+
+impl<T: Stream + Unpin> Stream for S<T> {
+    type Item = T::Item;
+
+    fn poll_next(mut self: Pin<&mut Self>, ctx: &mut Context) -> Poll<Option<Self::Item>> {
+        unsafe { Pin::new_unchecked(&mut self.0) }.poll_next(ctx)
+    }
+}
+
+struct StrictOnce {
+    polled: bool,
+}
+
+impl Stream for StrictOnce {
+    type Item = ();
+
+    fn poll_next(mut self: Pin<&mut Self>, _: &mut Context) -> Poll<Option<Self::Item>> {
+        assert!(!self.polled, "Polled after completion!");
+        self.polled = true;
+        Poll::Ready(None)
+    }
+}
+
+struct Interchanger {
+    polled: bool,
+}
+
+impl Stream for Interchanger {
+    type Item = S<Box<dyn Stream<Item = ()> + Unpin>>;
+
+    fn poll_next(mut self: Pin<&mut Self>, ctx: &mut Context) -> Poll<Option<Self::Item>> {
+        if self.polled {
+            self.polled = false;
+            ctx.waker().wake_by_ref();
+            Poll::Pending
+        } else {
+            self.polled = true;
+            Poll::Ready(Some(S(Box::new(StrictOnce { polled: false }))))
+        }
+    }
+}
+
+#[test]
+fn flat_map_doesnt_poll_completed_inner_stream() {
+    task::block_on(async {
+        assert_eq!(
+            Interchanger { polled: false }
+                .take(2)
+                .flat_map(identity)
+                .count()
+                .await,
+            0
+        );
+    });
+}
+
+#[test]
+fn flatten_doesnt_poll_completed_inner_stream() {
+    task::block_on(async {
+        assert_eq!(
+            Interchanger { polled: false }
+                .take(2)
+                .flatten()
+                .count()
+                .await,
+            0
+        );
+    });
+}