diff --git a/src/stream/stream/all.rs b/src/stream/stream/all.rs
index 62710240..3b65fc76 100644
--- a/src/stream/stream/all.rs
+++ b/src/stream/stream/all.rs
@@ -1,43 +1,36 @@
-use crate::future::Future;
-use crate::task::{Context, Poll};
-
 use std::marker::PhantomData;
 use std::pin::Pin;
 
-#[derive(Debug)]
-pub struct AllFuture<'a, S, F, T>
-where
-    F: FnMut(T) -> bool,
-{
+use crate::future::Future;
+use crate::stream::Stream;
+use crate::task::{Context, Poll};
+
+#[doc(hidden)]
+#[allow(missing_debug_implementations)]
+pub struct AllFuture<'a, S, F, T> {
     pub(crate) stream: &'a mut S,
     pub(crate) f: F,
     pub(crate) result: bool,
-    pub(crate) __item: PhantomData<T>,
+    pub(crate) _marker: PhantomData<T>,
 }
 
-impl<'a, S, F, T> AllFuture<'a, S, F, T>
-where
-    F: FnMut(T) -> bool,
-{
-    pin_utils::unsafe_pinned!(stream: &'a mut S);
-    pin_utils::unsafe_unpinned!(result: bool);
-    pin_utils::unsafe_unpinned!(f: F);
-}
+impl<S: Unpin, F, T> Unpin for AllFuture<'_, S, F, T> {}
 
 impl<S, F> Future for AllFuture<'_, S, F, S::Item>
 where
-    S: futures_core::stream::Stream + Unpin + Sized,
+    S: Stream + Unpin + Sized,
     F: FnMut(S::Item) -> bool,
 {
     type Output = bool;
 
     fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
-        use futures_core::stream::Stream;
-        let next = futures_core::ready!(self.as_mut().stream().poll_next(cx));
+        let next = futures_core::ready!(Pin::new(&mut *self.stream).poll_next(cx));
+
         match next {
             Some(v) => {
-                let result = (self.as_mut().f())(v);
-                *self.as_mut().result() = result;
+                let result = (&mut self.f)(v);
+                self.result = result;
+
                 if result {
                     // don't forget to wake this task again to pull the next item from stream
                     cx.waker().wake_by_ref();
diff --git a/src/stream/stream/any.rs b/src/stream/stream/any.rs
index f1f551a1..a23adf4b 100644
--- a/src/stream/stream/any.rs
+++ b/src/stream/stream/any.rs
@@ -1,43 +1,36 @@
-use crate::future::Future;
-use crate::task::{Context, Poll};
-
 use std::marker::PhantomData;
 use std::pin::Pin;
 
-#[derive(Debug)]
-pub struct AnyFuture<'a, S, F, T>
-where
-    F: FnMut(T) -> bool,
-{
+use crate::future::Future;
+use crate::stream::Stream;
+use crate::task::{Context, Poll};
+
+#[doc(hidden)]
+#[allow(missing_debug_implementations)]
+pub struct AnyFuture<'a, S, F, T> {
     pub(crate) stream: &'a mut S,
     pub(crate) f: F,
     pub(crate) result: bool,
-    pub(crate) __item: PhantomData<T>,
+    pub(crate) _marker: PhantomData<T>,
 }
 
-impl<'a, S, F, T> AnyFuture<'a, S, F, T>
-where
-    F: FnMut(T) -> bool,
-{
-    pin_utils::unsafe_pinned!(stream: &'a mut S);
-    pin_utils::unsafe_unpinned!(result: bool);
-    pin_utils::unsafe_unpinned!(f: F);
-}
+impl<S: Unpin, F, T> Unpin for AnyFuture<'_, S, F, T> {}
 
 impl<S, F> Future for AnyFuture<'_, S, F, S::Item>
 where
-    S: futures_core::stream::Stream + Unpin + Sized,
+    S: Stream + Unpin + Sized,
     F: FnMut(S::Item) -> bool,
 {
     type Output = bool;
 
     fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
-        use futures_core::stream::Stream;
-        let next = futures_core::ready!(self.as_mut().stream().poll_next(cx));
+        let next = futures_core::ready!(Pin::new(&mut *self.stream).poll_next(cx));
+
         match next {
             Some(v) => {
-                let result = (self.as_mut().f())(v);
-                *self.as_mut().result() = result;
+                let result = (&mut self.f)(v);
+                self.result = result;
+
                 if result {
                     Poll::Ready(true)
                 } else {
diff --git a/src/stream/stream/min_by.rs b/src/stream/stream/min_by.rs
index f63d52b8..a68cf313 100644
--- a/src/stream/stream/min_by.rs
+++ b/src/stream/stream/min_by.rs
@@ -2,8 +2,10 @@ use std::cmp::Ordering;
 use std::pin::Pin;
 
 use crate::future::Future;
+use crate::stream::Stream;
 use crate::task::{Context, Poll};
 
+#[doc(hidden)]
 #[allow(missing_debug_implementations)]
 pub struct MinByFuture<S, F, T> {
     stream: S,
@@ -27,7 +29,7 @@ impl<S, F, T> MinByFuture<S, F, T> {
 
 impl<S, F> Future for MinByFuture<S, F, S::Item>
 where
-    S: futures_core::stream::Stream + Unpin + Sized,
+    S: Stream + Unpin + Sized,
     S::Item: Copy,
     F: FnMut(&S::Item, &S::Item) -> Ordering,
 {
diff --git a/src/stream/stream/mod.rs b/src/stream/stream/mod.rs
index 462aeaed..fb8b38d6 100644
--- a/src/stream/stream/mod.rs
+++ b/src/stream/stream/mod.rs
@@ -44,9 +44,12 @@ use nth::NthFuture;
 
 use std::cmp::Ordering;
 use std::marker::PhantomData;
+use std::pin::Pin;
 
 use cfg_if::cfg_if;
 
+use crate::task::{Context, Poll};
+
 cfg_if! {
     if #[cfg(feature = "docs")] {
         #[doc(hidden)]
@@ -83,6 +86,55 @@ pub trait Stream {
     /// The type of items yielded by this stream.
     type Item;
 
+    /// Attempts to receive the next item from the stream.
+    ///
+    /// There are several possible return values:
+    ///
+    /// * `Poll::Pending` means this stream's next value is not ready yet.
+    /// * `Poll::Ready(None)` means this stream has been exhausted.
+    /// * `Poll::Ready(Some(item))` means `item` was received out of the stream.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// # fn main() { async_std::task::block_on(async {
+    /// #
+    /// use std::pin::Pin;
+    ///
+    /// use async_std::prelude::*;
+    /// use async_std::stream;
+    /// use async_std::task::{Context, Poll};
+    ///
+    /// fn increment(s: impl Stream<Item = i32> + Unpin) -> impl Stream<Item = i32> + Unpin {
+    ///     struct Increment<S>(S);
+    ///
+    ///     impl<S: Stream<Item = i32> + Unpin> Stream for Increment<S> {
+    ///         type Item = S::Item;
+    ///
+    ///         fn poll_next(
+    ///             mut self: Pin<&mut Self>,
+    ///             cx: &mut Context<'_>,
+    ///         ) -> Poll<Option<Self::Item>> {
+    ///             match Pin::new(&mut self.0).poll_next(cx) {
+    ///                 Poll::Pending => Poll::Pending,
+    ///                 Poll::Ready(None) => Poll::Ready(None),
+    ///                 Poll::Ready(Some(item)) => Poll::Ready(Some(item + 1)),
+    ///             }
+    ///         }
+    ///     }
+    ///
+    ///     Increment(s)
+    /// }
+    ///
+    /// let mut s = increment(stream::once(7));
+    ///
+    /// assert_eq!(s.next().await, Some(8));
+    /// assert_eq!(s.next().await, None);
+    /// #
+    /// # }) }
+    /// ```
+    fn poll_next(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Option<Self::Item>>;
+
     /// Advances the stream and returns the next value.
     ///
     /// Returns [`None`] when iteration is finished. Individual stream implementations may
@@ -108,7 +160,10 @@ pub trait Stream {
     /// ```
     fn next(&mut self) -> ret!('_, NextFuture, Option<Self::Item>)
     where
-        Self: Unpin;
+        Self: Unpin,
+    {
+        NextFuture { stream: self }
+    }
 
     /// Creates a stream that yields its first `n` elements.
     ///
@@ -312,13 +367,13 @@ pub trait Stream {
     #[inline]
     fn all<F>(&mut self, f: F) -> ret!('_, AllFuture, bool, F, Self::Item)
     where
-        Self: Sized,
+        Self: Unpin + Sized,
         F: FnMut(Self::Item) -> bool,
     {
         AllFuture {
             stream: self,
             result: true, // the default if the empty stream
-            __item: PhantomData,
+            _marker: PhantomData,
             f,
         }
     }
@@ -436,13 +491,13 @@ pub trait Stream {
     #[inline]
     fn any<F>(&mut self, f: F) -> ret!('_, AnyFuture, bool, F, Self::Item)
     where
-        Self: Sized,
+        Self: Unpin + Sized,
         F: FnMut(Self::Item) -> bool,
     {
         AnyFuture {
             stream: self,
             result: false, // the default if the empty stream
-            __item: PhantomData,
+            _marker: PhantomData,
             f,
         }
     }
@@ -451,10 +506,7 @@ pub trait Stream {
 impl<T: futures_core::stream::Stream + Unpin + ?Sized> Stream for T {
     type Item = <Self as futures_core::stream::Stream>::Item;
 
-    fn next(&mut self) -> ret!('_, NextFuture, Option<Self::Item>)
-    where
-        Self: Unpin,
-    {
-        NextFuture { stream: self }
+    fn poll_next(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Option<Self::Item>> {
+        futures_core::stream::Stream::poll_next(self, cx)
     }
 }
diff --git a/src/stream/stream/next.rs b/src/stream/stream/next.rs
index b64750d0..de75f5e9 100644
--- a/src/stream/stream/next.rs
+++ b/src/stream/stream/next.rs
@@ -1,6 +1,8 @@
+use std::pin::Pin;
+
 use crate::future::Future;
+use crate::stream::Stream;
 use crate::task::{Context, Poll};
-use std::pin::Pin;
 
 #[doc(hidden)]
 #[allow(missing_debug_implementations)]
@@ -8,7 +10,7 @@ pub struct NextFuture<'a, T: Unpin + ?Sized> {
     pub(crate) stream: &'a mut T,
 }
 
-impl<T: futures_core::stream::Stream + Unpin + ?Sized> Future for NextFuture<'_, T> {
+impl<T: Stream + Unpin + ?Sized> Future for NextFuture<'_, T> {
     type Output = Option<T::Item>;
 
     fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
diff --git a/src/stream/stream/take.rs b/src/stream/stream/take.rs
index 0499a6ac..0dea1d0c 100644
--- a/src/stream/stream/take.rs
+++ b/src/stream/stream/take.rs
@@ -1,7 +1,8 @@
-use crate::task::{Context, Poll};
-
 use std::pin::Pin;
 
+use crate::stream::Stream;
+use crate::task::{Context, Poll};
+
 /// A stream that yields the first `n` items of another stream.
 #[derive(Clone, Debug)]
 pub struct Take<S> {
@@ -11,12 +12,12 @@ pub struct Take<S> {
 
 impl<S: Unpin> Unpin for Take<S> {}
 
-impl<S: futures_core::stream::Stream> Take<S> {
+impl<S: Stream> Take<S> {
     pin_utils::unsafe_pinned!(stream: S);
     pin_utils::unsafe_unpinned!(remaining: usize);
 }
 
-impl<S: futures_core::stream::Stream> futures_core::stream::Stream for Take<S> {
+impl<S: Stream> futures_core::stream::Stream for Take<S> {
     type Item = S::Item;
 
     fn poll_next(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Option<S::Item>> {