diff --git a/tokio/src/sync/semaphore.rs b/tokio/src/sync/semaphore.rs
index fb907b6b5..7a060075d 100644
--- a/tokio/src/sync/semaphore.rs
+++ b/tokio/src/sync/semaphore.rs
@@ -47,7 +47,7 @@ use std::sync::Arc;
 /// }
 /// ```
 ///
-/// ## Limit the number of simultaneously opened files in your program.
+/// ## Limit the number of simultaneously opened files in your program
 ///
 /// Most operating systems have limits on the number of open file
 /// handles. Even in systems without explicit limits, resource constraints
@@ -76,7 +76,7 @@ use std::sync::Arc;
 /// }
 /// ```
 ///
-/// ## Limit the number of incoming requests being handled at the same time.
+/// ## Limit the number of incoming requests being handled at the same time
 ///
 /// Similar to limiting the number of simultaneously opened files, network handles
 /// are a limited resource. Allowing an unbounded amount of requests to be processed
@@ -125,19 +125,23 @@ use std::sync::Arc;
 ///
 /// ## Prevent tests from running in parallel
 ///
-/// By default, Rust runs tests in the same file in parallel. However, in some cases, running two tests in parallel may lead to problems.
-/// For example, this can happen when tests use the same database.
+/// By default, Rust runs tests in the same file in parallel. However, in some
+/// cases, running two tests in parallel may lead to problems. For example, this
+/// can happen when tests use the same database.
 ///
 /// Consider the following scenario:
-/// 1. `test_insert`: Inserts a key-value pair into the database, then retrieves the value using the same key to verify the insertion.
-/// 2. `test_update`: Inserts a key, then updates the key to a new value and verifies that the value has been accurately updated.
-/// 3. `test_others`: A third test that doesn't modify the database state. It can run in parallel with the other tests.
+/// 1. `test_insert`: Inserts a key-value pair into the database, then retrieves
+///    the value using the same key to verify the insertion.
+/// 2. `test_update`: Inserts a key, then updates the key to a new value and
+///    verifies that the value has been accurately updated.
+/// 3. `test_others`: A third test that doesn't modify the database state. It
+///    can run in parallel with the other tests.
 ///
-/// In this example, `test_insert` and `test_update` need to run in sequence to work, but it doesn't matter which test runs first.
-/// We can leverage a semaphore with a single permit to address this challenge.
+/// In this example, `test_insert` and `test_update` need to run in sequence to
+/// work, but it doesn't matter which test runs first. We can leverage a
+/// semaphore with a single permit to address this challenge.
 ///
 /// ```
-/// use tokio::sync::Semaphore;
 /// # use tokio::sync::Mutex;
 /// # use std::collections::BTreeMap;
 /// # struct Database {
@@ -164,6 +168,7 @@ use std::sync::Arc;
 /// #        *self.map.lock().await.get(key).unwrap()
 /// #    }
 /// # }
+/// use tokio::sync::Semaphore;
 ///
 /// // Initialize a static semaphore with only one permit, which is used to
 /// // prevent test_insert and test_update from running in parallel.
@@ -173,7 +178,7 @@ use std::sync::Arc;
 /// static DB: Database = Database::setup();
 ///
 /// #[tokio::test]
-/// # async fn fake_test() {}
+/// # async fn fake_test_insert() {}
 /// async fn test_insert() {
 ///     // Acquire permit before proceeding. Since the semaphore has only one permit,
 ///     // the test will wait if the permit is already acquired by other tests.
@@ -196,7 +201,7 @@ use std::sync::Arc;
 /// }
 ///
 /// #[tokio::test]
-/// # async fn fake_test() {}
+/// # async fn fake_test_update() {}
 /// async fn test_update() {
 ///     // Acquire permit before proceeding. Since the semaphore has only one permit,
 ///     // the test will wait if the permit is already acquired by other tests.
@@ -221,12 +226,12 @@ use std::sync::Arc;
 /// }
 ///
 /// #[tokio::test]
-/// # async fn fake_test() {}
+/// # async fn fake_test_others() {}
 /// async fn test_others() {
 ///     // This test can run in parallel with test_insert and test_update,
 ///     // so it does not use PERMIT.
 /// }
-/// # #[tokio::main]
+/// # #[tokio::main(flavor = "current_thread")]
 /// # async fn main() {
 /// #   test_insert().await;
 /// #   test_update().await;
@@ -236,6 +241,8 @@ use std::sync::Arc;
 ///
 /// ## Rate limiting using a token bucket
 ///
+/// This example showcases the [`add_permits`] and [`SemaphorePermit::forget`] methods.
+///
 /// Many applications and systems have constraints on the rate at which certain
 /// operations should occur. Exceeding this rate can result in suboptimal
 /// performance or even errors.
@@ -256,6 +263,8 @@ use std::sync::Arc;
 /// lot of cpu constantly looping and sleeping.
 ///
 /// [token bucket]: https://en.wikipedia.org/wiki/Token_bucket
+/// [`add_permits`]: crate::sync::Semaphore::add_permits
+/// [`SemaphorePermit::forget`]: crate::sync::SemaphorePermit::forget
 /// ```
 /// use std::sync::Arc;
 /// use tokio::sync::Semaphore;
@@ -292,8 +301,11 @@ use std::sync::Arc;
 ///
 ///     async fn acquire(&self) {
 ///         // This can return an error if the semaphore is closed, but we
-///         // never close it, so just ignore errors.
-///         let _ = self.sem.acquire().await;
+///         // never close it, so this error can never happen.
+///         let permit = self.sem.acquire().await.unwrap();
+///         // To avoid releasing the permit back to the semaphore, we use
+///         // the `SemaphorePermit::forget` method.
+///         permit.forget();
 ///     }
 /// }
 ///