diff --git a/futures-util/src/async_await/random.rs b/futures-util/src/async_await/random.rs
index 4f8c7254b4..0378fe9fc6 100644
--- a/futures-util/src/async_await/random.rs
+++ b/futures-util/src/async_await/random.rs
@@ -1,10 +1,6 @@
-use std::{
-    cell::Cell,
-    collections::hash_map::DefaultHasher,
-    hash::Hasher,
-    num::Wrapping,
-    sync::atomic::{AtomicUsize, Ordering},
-};
+use core::sync::atomic::{AtomicUsize, Ordering};
+#[cfg(feature = "std")]
+use std::cell::Cell;
 
 // Based on [Fisher–Yates shuffle].
 //
@@ -18,37 +14,86 @@ pub fn shuffle<T>(slice: &mut [T]) {
 
 /// Return a value from `0..n`.
 fn gen_index(n: usize) -> usize {
-    (random() % n as u64) as usize
+    random() % n
 }
 
-/// Pseudorandom number generator based on [xorshift*].
+/// Pseudorandom number generator based on [xorshift].
 ///
-/// [xorshift*]: https://en.wikipedia.org/wiki/Xorshift#xorshift*
-fn random() -> u64 {
-    thread_local! {
-        static RNG: Cell<Wrapping<u64>> = Cell::new(Wrapping(prng_seed()));
-    }
-
-    fn prng_seed() -> u64 {
+/// [xorshift]: https://en.wikipedia.org/wiki/Xorshift
+fn random() -> usize {
+    #[cfg(feature = "std")]
+    fn prng_seed() -> usize {
         static COUNTER: AtomicUsize = AtomicUsize::new(0);
 
         // Any non-zero seed will do
         let mut seed = 0;
         while seed == 0 {
-            let mut hasher = DefaultHasher::new();
-            hasher.write_usize(COUNTER.fetch_add(1, Ordering::Relaxed));
-            seed = hasher.finish();
+            seed = COUNTER.fetch_add(1, Ordering::Relaxed);
         }
         seed
     }
 
-    RNG.with(|rng| {
-        let mut x = rng.get();
-        debug_assert_ne!(x.0, 0);
+    /// [xorshift*] is used on 64bit platforms.
+    ///
+    /// [xorshift*]: https://en.wikipedia.org/wiki/Xorshift#xorshift*
+    #[cfg(target_pointer_width = "64")]
+    fn xorshift(mut x: usize) -> (usize, usize) {
+        debug_assert_ne!(x, 0);
         x ^= x >> 12;
         x ^= x << 25;
         x ^= x >> 27;
-        rng.set(x);
-        x.0.wrapping_mul(0x2545_f491_4f6c_dd1d)
-    })
+        (
+            x,
+            x.wrapping_mul(0x2545_f491_4f6c_dd1d),
+        )
+    }
+
+    /// [xorshift32] is used on 32bit platforms.
+    ///
+    /// [xorshift32]: https://en.wikipedia.org/wiki/Xorshift
+    #[cfg(target_pointer_width = "32")]
+    fn xorshift(mut x: usize) -> (usize, usize) {
+        debug_assert_ne!(x, 0);
+        x ^= x << 13;
+        x ^= x >> 17;
+        x ^= x << 5;
+        (x, x)
+    }
+
+    /// A non-standard xorshift variant is used on 16bit platforms.
+    #[cfg(target_pointer_width = "16")]
+    fn xorshift(mut x: usize) -> (usize, usize) {
+        // Constants chosen from: http://b2d-f9r.blogspot.com/2010/08/16-bit-xorshift-rng.html
+        debug_assert_ne!(x, 0);
+        x ^= x << 4;
+        x ^= x >> 3;
+        x ^= x << 7;
+        (x, x)
+    }
+
+    #[cfg(feature = "std")]
+    fn rng() -> usize {
+        thread_local! {
+            static RNG: Cell<usize> = Cell::new(prng_seed());
+        }
+
+        RNG.with(|rng| {
+            let (x, res) = xorshift(rng.get());
+            rng.set(x);
+            res
+        })
+    }
+
+    #[cfg(not(feature = "std"))]
+    fn rng() -> usize {
+        // A deterministic seed is used in absense of TLS
+        static RNG: AtomicUsize = AtomicUsize::new(42);
+
+        // Preemption here can cause multiple threads to observe repeated state
+        let (x, res) = xorshift(RNG.load(Ordering::Relaxed));
+        RNG.store(x, Ordering::Relaxed);
+        res
+    }
+
+    rng()
 }
diff --git a/futures-util/src/lib.rs b/futures-util/src/lib.rs
index 44a995fc9c..21645b148d 100644
--- a/futures-util/src/lib.rs
+++ b/futures-util/src/lib.rs
@@ -39,12 +39,10 @@ pub use futures_core::ready;
 pub use pin_utils::pin_mut;
 
 // Not public API.
-#[cfg(feature = "std")]
 #[cfg(feature = "async-await")]
 #[macro_use]
 #[doc(hidden)]
 pub mod async_await;
-#[cfg(feature = "std")]
 #[cfg(feature = "async-await")]
 #[doc(hidden)]
 pub use self::async_await::*;
diff --git a/futures/src/lib.rs b/futures/src/lib.rs
index d4f248257a..bfeebf04f9 100644
--- a/futures/src/lib.rs
+++ b/futures/src/lib.rs
@@ -542,13 +542,11 @@ pub mod never {
 pub use futures_core::core_reexport;
 
 // Not public API.
-#[cfg(feature = "std")]
 #[cfg(feature = "async-await")]
 #[doc(hidden)]
 pub use futures_util::async_await;
 
 // Not public API.
-#[cfg(feature = "std")]
 #[cfg(feature = "async-await")]
 #[doc(hidden)]
 pub mod inner_macro {
@@ -558,7 +556,6 @@ pub mod inner_macro {
     pub use futures_util::select_biased;
 }
 
-#[cfg(feature = "std")]
 #[cfg(feature = "async-await")]
 futures_util::document_join_macro! {
     #[macro_export]
@@ -582,7 +579,6 @@ futures_util::document_join_macro! {
     }
 }
 
-#[cfg(feature = "std")]
 #[cfg(feature = "async-await")]
 futures_util::document_select_macro! {
     #[macro_export]