diff --git a/futures-util/Cargo.toml b/futures-util/Cargo.toml
index ed1b0e3199..daf46c26ae 100644
--- a/futures-util/Cargo.toml
+++ b/futures-util/Cargo.toml
@@ -12,8 +12,7 @@ Common utilities and extension traits for the futures-rs library.
 
 [features]
 default = ["std", "async-await", "async-await-macro"]
-std = ["alloc", "futures-core/std", "futures-task/std", "rand/std", "rand/std_rng", "slab"]
-getrandom = ["rand/getrandom"]
+std = ["alloc", "futures-core/std", "futures-task/std", "slab"]
 alloc = ["futures-core/alloc", "futures-task/alloc"]
 async-await = []
 async-await-macro = ["async-await", "futures-macro"]
@@ -44,7 +43,6 @@ futures_01 = { version = "0.1.25", optional = true, package = "futures" }
 tokio-io = { version = "0.1.9", optional = true }
 pin-utils = "0.1.0"
 pin-project-lite = "0.2.6"
-rand = { version = "0.8.5", default-features = false, features = ["small_rng"] }
 
 [dev-dependencies]
 futures = { path = "../futures", features = ["async-await", "thread-pool"] }
diff --git a/futures-util/src/async_await/mod.rs b/futures-util/src/async_await/mod.rs
index 7276da227a..94a93e6f4c 100644
--- a/futures-util/src/async_await/mod.rs
+++ b/futures-util/src/async_await/mod.rs
@@ -38,11 +38,9 @@ mod stream_select_mod;
 pub use self::stream_select_mod::*;
 
 #[cfg(feature = "std")]
-#[cfg(feature = "async-await-macro")]
 mod random;
 #[allow(unreachable_pub)] // https://github.com/rust-lang/rust/issues/64762
 #[cfg(feature = "std")]
-#[cfg(feature = "async-await-macro")]
 pub use self::random::*;
 
 #[doc(hidden)]
diff --git a/futures-util/src/async_await/random.rs b/futures-util/src/async_await/random.rs
index 4f8c7254b4..a799ef0a1e 100644
--- a/futures-util/src/async_await/random.rs
+++ b/futures-util/src/async_await/random.rs
@@ -17,7 +17,7 @@ pub fn shuffle<T>(slice: &mut [T]) {
 }
 
 /// Return a value from `0..n`.
-fn gen_index(n: usize) -> usize {
+pub(crate) fn gen_index(n: usize) -> usize {
     (random() % n as u64) as usize
 }
 
diff --git a/futures-util/src/future/select.rs b/futures-util/src/future/select.rs
index 6eeb4fd811..6bb9b80fc1 100644
--- a/futures-util/src/future/select.rs
+++ b/futures-util/src/future/select.rs
@@ -3,15 +3,12 @@ use crate::future::{Either, FutureExt};
 use core::pin::Pin;
 use futures_core::future::{FusedFuture, Future};
 use futures_core::task::{Context, Poll};
-use rand::rngs::SmallRng;
-use rand::Rng;
 
 /// Future for the [`select()`] function.
 #[must_use = "futures do nothing unless you `.await` or poll them"]
 #[derive(Debug)]
 pub struct Select<A, B> {
     inner: Option<(A, B)>,
-    rng: SmallRng,
 }
 
 impl<A: Unpin, B: Unpin> Unpin for Select<A, B> {}
@@ -94,7 +91,6 @@ where
 {
     assert_future::<Either<(A::Output, B), (B::Output, A)>, _>(Select {
         inner: Some((future1, future2)),
-        rng: crate::gen_rng(),
     })
 }
 
@@ -116,7 +112,6 @@ where
             }
         }
 
-        let a_polls_first = self.rng.gen::<bool>();
         let (a, b) = self.inner.as_mut().expect("cannot poll Select twice");
 
         macro_rules! poll_wrap {
@@ -127,13 +122,20 @@ where
             };
         }
 
-        if a_polls_first {
+        #[cfg(feature = "std")]
+        if crate::gen_index(2) == 0 {
             poll_wrap!(a, unwrap_option(self.inner.take()).1, Either::Left);
             poll_wrap!(b, unwrap_option(self.inner.take()).0, Either::Right);
         } else {
             poll_wrap!(b, unwrap_option(self.inner.take()).0, Either::Right);
             poll_wrap!(a, unwrap_option(self.inner.take()).1, Either::Left);
         }
+
+        #[cfg(not(feature = "std"))]
+        {
+            poll_wrap!(a, unwrap_option(self.inner.take()).1, Either::Left);
+            poll_wrap!(b, unwrap_option(self.inner.take()).0, Either::Right);
+        }
         Poll::Pending
     }
 }
diff --git a/futures-util/src/future/select_ok.rs b/futures-util/src/future/select_ok.rs
index 3043f91e14..00349614f2 100644
--- a/futures-util/src/future/select_ok.rs
+++ b/futures-util/src/future/select_ok.rs
@@ -6,15 +6,12 @@ use core::mem;
 use core::pin::Pin;
 use futures_core::future::{Future, TryFuture};
 use futures_core::task::{Context, Poll};
-use rand::prelude::SliceRandom;
-use rand::rngs::SmallRng;
 
 /// Future for the [`select_ok`] function.
 #[derive(Debug)]
 #[must_use = "futures do nothing unless you `.await` or poll them"]
 pub struct SelectOk<Fut> {
     inner: Vec<Fut>,
-    rng: SmallRng,
 }
 
 impl<Fut: Unpin> Unpin for SelectOk<Fut> {}
@@ -48,7 +45,7 @@ where
     I: IntoIterator,
     I::Item: TryFuture + Unpin,
 {
-    let ret = SelectOk { inner: iter.into_iter().collect(), rng: crate::gen_rng() };
+    let ret = SelectOk { inner: iter.into_iter().collect() };
     assert!(!ret.inner.is_empty(), "iterator provided to select_ok was empty");
     assert_future::<
         Result<(<I::Item as TryFuture>::Ok, Vec<I::Item>), <I::Item as TryFuture>::Error>,
@@ -60,8 +57,9 @@ impl<Fut: TryFuture + Unpin> Future for SelectOk<Fut> {
     type Output = Result<(Fut::Ok, Vec<Fut>), Fut::Error>;
 
     fn poll(mut self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
-        let Self { inner, rng } = &mut *self;
-        inner.shuffle(rng);
+        let Self { inner } = &mut *self;
+        #[cfg(feature = "std")]
+        crate::shuffle(inner);
         // loop until we've either exhausted all errors, a success was hit, or nothing is ready
         loop {
             let item = inner.iter_mut().enumerate().find_map(|(i, f)| match f.try_poll_unpin(cx) {
@@ -74,7 +72,7 @@ impl<Fut: TryFuture + Unpin> Future for SelectOk<Fut> {
                     drop(inner.remove(idx));
                     match res {
                         Ok(e) => {
-                            let rest = mem::take(&mut self.inner);
+                            let rest = mem::take(inner);
                             return Poll::Ready(Ok((e, rest)));
                         }
                         Err(e) => {
diff --git a/futures-util/src/future/try_select.rs b/futures-util/src/future/try_select.rs
index cbef1290d6..f2811bf364 100644
--- a/futures-util/src/future/try_select.rs
+++ b/futures-util/src/future/try_select.rs
@@ -2,15 +2,12 @@ use crate::future::{Either, TryFutureExt};
 use core::pin::Pin;
 use futures_core::future::{Future, TryFuture};
 use futures_core::task::{Context, Poll};
-use rand::rngs::SmallRng;
-use rand::Rng;
 
 /// Future for the [`try_select()`] function.
 #[must_use = "futures do nothing unless you `.await` or poll them"]
 #[derive(Debug)]
 pub struct TrySelect<A, B> {
     inner: Option<(A, B)>,
-    rng: SmallRng,
 }
 
 impl<A: Unpin, B: Unpin> Unpin for TrySelect<A, B> {}
@@ -63,7 +60,6 @@ where
 {
     super::assert_future::<Result<EitherOk<A, B>, EitherErr<A, B>>, _>(TrySelect {
         inner: Some((future1, future2)),
-        rng: crate::gen_rng(),
     })
 }
 
@@ -92,10 +88,17 @@ where
                 }
             };
         }
-        if self.rng.gen::<bool>() {
+
+        #[cfg(feature = "std")]
+        if crate::gen_index(2) == 0 {
             poll_wrap!(a, b, Either::Left, Either::Right)
         } else {
             poll_wrap!(b, a, Either::Right, Either::Left)
         }
+
+        #[cfg(not(feature = "std"))]
+        {
+            poll_wrap!(a, b, Either::Left, Either::Right)
+        }
     }
 }
diff --git a/futures-util/src/lib.rs b/futures-util/src/lib.rs
index d1621ec85a..d03252d7cd 100644
--- a/futures-util/src/lib.rs
+++ b/futures-util/src/lib.rs
@@ -31,8 +31,6 @@ extern crate alloc;
 // Macro re-exports
 pub use futures_core::ready;
 pub use pin_utils::pin_mut;
-use rand::rngs::SmallRng;
-use rand::SeedableRng;
 
 #[cfg(feature = "async-await")]
 #[macro_use]
@@ -338,18 +336,3 @@ mod abortable;
 
 mod fns;
 mod unfold_state;
-
-fn gen_rng() -> SmallRng {
-    #[cfg(feature = "std")]
-    {
-        SmallRng::from_rng(rand::thread_rng()).expect("generating SmallRng via thread_rng failed")
-    }
-    #[cfg(all(feature = "getrandom", not(feature = "std")))]
-    {
-        SmallRng::from_entropy()
-    }
-    #[cfg(not(any(feature = "getrandom", feature = "std")))]
-    {
-        SmallRng::seed_from_u64(0)
-    }
-}