diff --git a/futures-util/src/future/first.rs b/futures-util/src/future/first.rs
index 92510823d7..9fa14e3008 100644
--- a/futures-util/src/future/first.rs
+++ b/futures-util/src/future/first.rs
@@ -1,6 +1,6 @@
 use crate::future::Either;
 use core::pin::Pin;
-use futures_core::future::{FusedFuture, Future};
+use futures_core::future::Future;
 use futures_core::task::{Context, Poll};
 use pin_utils::unsafe_pinned;
 
@@ -12,6 +12,8 @@ pub struct First<F1, F2> {
     future2: F2,
 }
 
+impl<F1: Unpin, F2: Unpin> Unpin for First<F1, F2> {}
+
 impl<F1, F2> First<F1, F2> {
     unsafe_pinned!(future1: F1);
     unsafe_pinned!(future2: F2);
@@ -32,12 +34,9 @@ impl<F1: Future, F2: Future> Future for First<F1, F2> {
     }
 }
 
-impl<F1: FusedFuture, F2: FusedFuture> FusedFuture for First<F1, F2> {
-    #[inline]
-    fn is_terminated(&self) -> bool {
-        self.future1.is_terminated() || self.future2.is_terminated()
-    }
-}
+// We don't provide FusedFuture, because the overhead of implementing it (
+// which requires a separate bool or Option field) is precisely the same as
+// calling .fuse()
 
 /// Waits for either one of two differently-typed futures to complete.
 ///
@@ -52,7 +51,7 @@ impl<F1: FusedFuture, F2: FusedFuture> FusedFuture for First<F1, F2> {
 /// wrapped version of them.
 ///
 /// Also note that if both this and the second future have the same
-/// output type you can use the `Either::factor_first` method to
+/// output type you can use the `Either::into_immer` method to
 /// conveniently extract out the value at the end.
 pub fn first<F1, F2>(future1: F1, future2: F2) -> First<F1, F2> {
     First { future1, future2 }
diff --git a/futures-util/src/future/first_all.rs b/futures-util/src/future/first_all.rs
index f679263478..13aa288108 100644
--- a/futures-util/src/future/first_all.rs
+++ b/futures-util/src/future/first_all.rs
@@ -1,6 +1,6 @@
 use core::iter::FromIterator;
 use core::pin::Pin;
-use futures_core::future::{FusedFuture, Future};
+use futures_core::future::Future;
 use futures_core::task::{Context, Poll};
 
 /// Future for the [`first_all()`] function.
@@ -32,26 +32,15 @@ impl<F: Future> Future for FirstAll<F> {
                 Poll::Pending => None,
             }
         }) {
-            Some(out) => {
-                // Safety: safe because vec clears in place
-                this.futures.clear();
-                Poll::Ready(out)
-            }
+            Some(out) => Poll::Ready(out),
             None => Poll::Pending,
         }
     }
 }
 
-impl<F: FusedFuture> FusedFuture for FirstAll<F> {
-    #[inline]
-    fn is_terminated(&self) -> bool {
-        // Logic: it's possible for a future to independently become
-        // terminated, before it returns Ready, so we're not terminated unless
-        // *all* of our inner futures are terminated. When our own poll returns
-        // Ready, this vector is cleared, so the logic works correctly.
-        self.futures.iter().all(|fut| fut.is_terminated())
-    }
-}
+// We don't provide FusedFuture, because the overhead of implementing it (
+// which requires clearing the vector after Ready is returned) is precisely
+// the same as using .fuse()
 
 impl<Fut: Future> FromIterator<Fut> for FirstAll<Fut> {
     fn from_iter<T: IntoIterator<Item = Fut>>(iter: T) -> Self {
diff --git a/futures-util/src/future/first_ok.rs b/futures-util/src/future/first_ok.rs
index 8be4369c5f..a25f6f1e12 100644
--- a/futures-util/src/future/first_ok.rs
+++ b/futures-util/src/future/first_ok.rs
@@ -23,17 +23,10 @@ impl<F: FusedFuture + TryFuture> Future for FirstOk<F> {
     #[inline]
     fn poll(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
         // Basic logic diagram:
-        // - If all existing futures are terminated, return Pending. This means
-        //   someone polled after this future returned ready, or that this
-        //   future will never return ready because a future spuriously
-        //   terminated itself.
-        // - If a future returns Ok, clear the vector (this is safe because
-        //   vec drops in place), then return that value. We clear the vector
-        //   so that our FusedFuture impl, which checks `are all futures
-        //   terminated`, works correctly.
+        // - If all existing futures are terminated, return Pending.
+        // - If a future returns Ok, return that value.
         // - If all existing futures BECOME terminated while polling them, and
-        //   an error was returned, return the final error; otherwise return
-        //   pending.
+        //   an error was returned, return the final error.
 
         /// Helper enum to track our state as we poll each future
         enum State<E> {
@@ -64,19 +57,15 @@ impl<F: FusedFuture + TryFuture> Future for FirstOk<F> {
         }
 
         let mut state = State::NoErrors;
-        let this = self.get_mut();
-        for fut in this.futures.iter_mut() {
+
+        for fut in self.get_mut().futures.iter_mut() {
             if !fut.is_terminated() {
                 // Safety: we promise that the future is never moved out of the vec,
                 // and that the vec never reallocates once FirstOk has been created
                 // (specifically after the first poll)
                 let pinned = unsafe { Pin::new_unchecked(fut) };
                 match pinned.try_poll(cx) {
-                    Poll::Ready(Ok(out)) => {
-                        // Safety: safe because vec clears in place
-                        this.futures.clear();
-                        return Poll::Ready(Ok(out));
-                    }
+                    Poll::Ready(Ok(out)) => return Poll::Ready(Ok(out)),
                     Poll::Ready(Err(err)) => state.apply_error(err),
                     Poll::Pending => state.apply_pending(),
                 }
@@ -85,17 +74,21 @@ impl<F: FusedFuture + TryFuture> Future for FirstOk<F> {
 
         match state {
             SeenError(err) => Poll::Ready(Err(err)),
-            NoErrors | SeenPending => Poll::Pending,
+            SeenPending => Poll::Pending,
+            // This is unreachable unless every future in the vec returned
+            // is_terminated, which means that we must have returned Ready on
+            // a previous poll, or the vec is empty, which we disallow in the
+            // first_ok constructor, or that we were initialized with futures
+            // that have already returned Ready, which is possibly unsound
+            // (given !Unpin futures) but certainly breaks first_ok contract.
+            NoErrors => panic!("All futures in the FirstOk terminated without a result being found. Did you re-poll after Ready?"),
         }
     }
 }
 
-impl<F: FusedFuture + TryFuture> FusedFuture for FirstOk<F> {
-    #[inline]
-    fn is_terminated(&self) -> bool {
-        self.futures.iter().all(|fut| fut.is_terminated())
-    }
-}
+// We don't provide FusedFuture, because the overhead of implementing it (
+// which requires clearing the vector after Ready is returned) is precisely
+// the same as using .fuse()
 
 impl<Fut: FusedFuture + TryFuture> FromIterator<Fut> for FirstOk<Fut> {
     fn from_iter<T: IntoIterator<Item = Fut>>(iter: T) -> Self {
@@ -121,13 +114,27 @@ impl<Fut: FusedFuture + TryFuture> FromIterator<Fut> for FirstOk<Fut> {
 ///
 /// # Panics
 ///
-/// This function will panic if the iterator specified contains no items.
+/// This function will panic if the iterator specified contains no items, or
+/// if any of the futures have already been terminated.
 pub fn first_ok<I>(futures: I) -> FirstOk<I::Item>
 where
     I: IntoIterator,
     I::Item: FusedFuture + TryFuture,
 {
-    let futures = Vec::from_iter(futures);
-    assert!(!futures.is_empty(), "Need at least 1 future for first_ok");
+    let futures: Vec<_> = futures
+        .into_iter()
+        .inspect(|fut| {
+            assert!(
+                !fut.is_terminated(),
+                "Can't call first_ok with a terminated future"
+            )
+        })
+        .collect();
+
+    assert!(
+        !futures.is_empty(),
+        "Need at least 1 non-terminated future for first_ok"
+    );
+
     FirstOk { futures }
 }