diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 88fa10f5fca..2813ede8a86 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -300,6 +300,8 @@ jobs:
         with:
           toolchain: ${{ env.rust_nightly }}
           components: rust-src
+      - name: Install cargo-hack
+        uses: taiki-e/install-action@cargo-hack
       # Install linker and libraries for i686-unknown-linux-gnu
       - uses: taiki-e/setup-cross-toolchain-action@v1
         with:
@@ -307,6 +309,14 @@ jobs:
       - run: cargo test -Zbuild-std --target target-specs/i686-unknown-linux-gnu.json -p tokio --all-features
         env:
           RUSTFLAGS: --cfg tokio_unstable -Dwarnings --cfg tokio_no_atomic_u64
+      # https://github.com/tokio-rs/tokio/pull/5356
+      # https://github.com/tokio-rs/tokio/issues/5373
+      - run: cargo hack build -p tokio --feature-powerset --depth 2 -Z avoid-dev-deps --keep-going
+        env:
+          RUSTFLAGS: --cfg tokio_unstable -Dwarnings --cfg tokio_no_atomic_u64 --cfg tokio_no_const_mutex_new
+      - run: cargo hack build -p tokio --feature-powerset --depth 2 -Z avoid-dev-deps --keep-going
+        env:
+          RUSTFLAGS: --cfg tokio_unstable -Dwarnings --cfg tokio_no_atomic_u64
 
   features:
     name: features
diff --git a/tokio/build.rs b/tokio/build.rs
index 503c0242fc8..ddade2876bb 100644
--- a/tokio/build.rs
+++ b/tokio/build.rs
@@ -27,12 +27,13 @@ const CONST_MUTEX_NEW_PROBE: &str = r#"
 const TARGET_HAS_ATOMIC_PROBE: &str = r#"
 {
     #[cfg(target_has_atomic = "ptr")]
-    let _ = (); 
+    let _ = ();
 }
 "#;
 
 const TARGET_ATOMIC_U64_PROBE: &str = r#"
 {
+    #[allow(unused_imports)]
     use std::sync::atomic::AtomicU64 as _;
 }
 "#;
diff --git a/tokio/src/util/mod.rs b/tokio/src/util/mod.rs
index 245e64de6b4..9f6119acbb5 100644
--- a/tokio/src/util/mod.rs
+++ b/tokio/src/util/mod.rs
@@ -6,7 +6,12 @@ cfg_io_driver! {
 #[cfg(feature = "rt")]
 pub(crate) mod atomic_cell;
 
-#[cfg(any(feature = "rt", feature = "signal", feature = "process"))]
+#[cfg(any(
+    feature = "rt",
+    feature = "signal",
+    feature = "process",
+    tokio_no_const_mutex_new,
+))]
 pub(crate) mod once_cell;
 
 #[cfg(any(