diff --git a/tokio/src/sync/once_cell.rs b/tokio/src/sync/once_cell.rs
index 1a2303e8e6a..82b8259c667 100644
--- a/tokio/src/sync/once_cell.rs
+++ b/tokio/src/sync/once_cell.rs
@@ -132,36 +132,22 @@ impl<T> OnceCell<T> {
         }
     }
 
-    /// Creates a new `OnceCell` that contains the provided value, if any.
+    /// Creates a new empty `OnceCell` instance.
     ///
-    /// If the `Option` is `None`, this is equivalent to `OnceCell::new`.
+    /// Equivalent to `OnceCell::new`, except that it can be used in static
+    /// variables.
     ///
-    /// [`OnceCell::new`]: crate::sync::OnceCell::new
-    // Once https://github.com/rust-lang/rust/issues/73255 lands
-    // and tokio MSRV is bumped to the rustc version with it stablised,
-    // we can made this function available in const context,
-    // by creating `Semaphore::const_new_closed`.
-    pub fn new_with(value: Option<T>) -> Self {
-        if let Some(v) = value {
-            OnceCell::from(v)
-        } else {
-            OnceCell::new()
-        }
-    }
-
-    /// Creates a new `OnceCell` that contains the provided value.
+    /// When using the `tracing` [unstable feature], a `OnceCell` created with
+    /// `const_new` will not be instrumented. As such, it will not be visible
+    /// in [`tokio-console`]. Instead, [`OnceCell::new`] should be used to
+    /// create an instrumented object if that is needed.
     ///
     /// # Example
     ///
-    /// When using the `tracing` [unstable feature], a `OnceCell` created with
-    /// `const_new_with` will not be instrumented. As such, it will not be
-    /// visible in [`tokio-console`]. Instead, [`OnceCell::new_with`] should be
-    /// used to create an instrumented object if that is needed.
-    ///
     /// ```
     /// use tokio::sync::OnceCell;
     ///
-    /// static ONCE: OnceCell<u32> = OnceCell::const_new_with(1);
+    /// static ONCE: OnceCell<u32> = OnceCell::const_new();
     ///
     /// async fn get_global_integer() -> &'static u32 {
     ///     ONCE.get_or_init(|| async {
@@ -172,37 +158,51 @@ impl<T> OnceCell<T> {
     /// #[tokio::main]
     /// async fn main() {
     ///     let result = get_global_integer().await;
-    ///     assert_eq!(*result, 1);
+    ///     assert_eq!(*result, 2);
     /// }
     /// ```
     ///
     /// [`tokio-console`]: https://github.com/tokio-rs/console
     /// [unstable feature]: crate#unstable-features
     #[cfg(not(all(loom, test)))]
-    pub const fn const_new_with(value: T) -> Self {
+    pub const fn const_new() -> Self {
         OnceCell {
-            value_set: AtomicBool::new(true),
-            value: UnsafeCell::new(MaybeUninit::new(value)),
-            semaphore: Semaphore::const_new_closed(),
+            value_set: AtomicBool::new(false),
+            value: UnsafeCell::new(MaybeUninit::uninit()),
+            semaphore: Semaphore::const_new(1),
         }
     }
 
-    /// Creates a new empty `OnceCell` instance.
+    /// Creates a new `OnceCell` that contains the provided value, if any.
     ///
-    /// Equivalent to `OnceCell::new`, except that it can be used in static
-    /// variables.
+    /// If the `Option` is `None`, this is equivalent to `OnceCell::new`.
     ///
-    /// When using the `tracing` [unstable feature], a `OnceCell` created with
-    /// `const_new` will not be instrumented. As such, it will not be visible
-    /// in [`tokio-console`]. Instead, [`OnceCell::new`] should be used to
-    /// create an instrumented object if that is needed.
+    /// [`OnceCell::new`]: crate::sync::OnceCell::new
+    // Once https://github.com/rust-lang/rust/issues/73255 lands
+    // and tokio MSRV is bumped to the rustc version with it stablised,
+    // we can made this function available in const context,
+    // by creating `Semaphore::const_new_closed`.
+    pub fn new_with(value: Option<T>) -> Self {
+        if let Some(v) = value {
+            OnceCell::from(v)
+        } else {
+            OnceCell::new()
+        }
+    }
+
+    /// Creates a new `OnceCell` that contains the provided value.
     ///
     /// # Example
     ///
+    /// When using the `tracing` [unstable feature], a `OnceCell` created with
+    /// `const_new_with` will not be instrumented. As such, it will not be
+    /// visible in [`tokio-console`]. Instead, [`OnceCell::new_with`] should be
+    /// used to create an instrumented object if that is needed.
+    ///
     /// ```
     /// use tokio::sync::OnceCell;
     ///
-    /// static ONCE: OnceCell<u32> = OnceCell::const_new();
+    /// static ONCE: OnceCell<u32> = OnceCell::const_new_with(1);
     ///
     /// async fn get_global_integer() -> &'static u32 {
     ///     ONCE.get_or_init(|| async {
@@ -213,18 +213,18 @@ impl<T> OnceCell<T> {
     /// #[tokio::main]
     /// async fn main() {
     ///     let result = get_global_integer().await;
-    ///     assert_eq!(*result, 2);
+    ///     assert_eq!(*result, 1);
     /// }
     /// ```
     ///
     /// [`tokio-console`]: https://github.com/tokio-rs/console
     /// [unstable feature]: crate#unstable-features
     #[cfg(not(all(loom, test)))]
-    pub const fn const_new() -> Self {
+    pub const fn const_new_with(value: T) -> Self {
         OnceCell {
-            value_set: AtomicBool::new(false),
-            value: UnsafeCell::new(MaybeUninit::uninit()),
-            semaphore: Semaphore::const_new(1),
+            value_set: AtomicBool::new(true),
+            value: UnsafeCell::new(MaybeUninit::new(value)),
+            semaphore: Semaphore::const_new_closed(),
         }
     }