diff --git a/library/std/src/ffi/os_str.rs b/library/std/src/ffi/os_str.rs
index 14914287cb1..ecaab670349 100644
--- a/library/std/src/ffi/os_str.rs
+++ b/library/std/src/ffi/os_str.rs
@@ -361,7 +361,7 @@ impl OsString {
 impl From<String> for OsString {
     /// Converts a [`String`] into a [`OsString`].
     ///
-    /// The conversion copies the data, and includes an allocation on the heap.
+    /// This conversion does not allocate or copy memory.
     #[inline]
     fn from(s: String) -> OsString {
         OsString { inner: Buf::from_string(s) }
@@ -858,7 +858,7 @@ impl From<Cow<'_, OsStr>> for Box<OsStr> {
 
 #[stable(feature = "os_string_from_box", since = "1.18.0")]
 impl From<Box<OsStr>> for OsString {
-    /// Converts a [`Box`]`<`[`OsStr`]`>` into a `OsString` without copying or
+    /// Converts a [`Box`]`<`[`OsStr`]`>` into an [`OsString`] without copying or
     /// allocating.
     #[inline]
     fn from(boxed: Box<OsStr>) -> OsString {
diff --git a/library/std/src/path.rs b/library/std/src/path.rs
index 57c892f32b1..f4020a42879 100644
--- a/library/std/src/path.rs
+++ b/library/std/src/path.rs
@@ -1467,7 +1467,7 @@ impl<T: ?Sized + AsRef<OsStr>> From<&T> for PathBuf {
 
 #[stable(feature = "rust1", since = "1.0.0")]
 impl From<OsString> for PathBuf {
-    /// Converts a `OsString` into a `PathBuf`
+    /// Converts an [`OsString`] into a [`PathBuf`]
     ///
     /// This conversion does not allocate or copy memory.
     #[inline]
@@ -1478,7 +1478,7 @@ impl From<OsString> for PathBuf {
 
 #[stable(feature = "from_path_buf_for_os_string", since = "1.14.0")]
 impl From<PathBuf> for OsString {
-    /// Converts a `PathBuf` into a `OsString`
+    /// Converts a [`PathBuf`] into an [`OsString`]
     ///
     /// This conversion does not allocate or copy memory.
     #[inline]
@@ -1489,7 +1489,7 @@ impl From<PathBuf> for OsString {
 
 #[stable(feature = "rust1", since = "1.0.0")]
 impl From<String> for PathBuf {
-    /// Converts a `String` into a `PathBuf`
+    /// Converts a [`String`] into a [`PathBuf`]
     ///
     /// This conversion does not allocate or copy memory.
     #[inline]
@@ -1595,7 +1595,7 @@ impl<'a> From<Cow<'a, Path>> for PathBuf {
 
 #[stable(feature = "shared_from_slice2", since = "1.24.0")]
 impl From<PathBuf> for Arc<Path> {
-    /// Converts a `PathBuf` into an `Arc` by moving the `PathBuf` data into a new `Arc` buffer.
+    /// Converts a [`PathBuf`] into an [`Arc`] by moving the [`PathBuf`] data into a new [`Arc`] buffer.
     #[inline]
     fn from(s: PathBuf) -> Arc<Path> {
         let arc: Arc<OsStr> = Arc::from(s.into_os_string());
@@ -1605,7 +1605,7 @@ impl From<PathBuf> for Arc<Path> {
 
 #[stable(feature = "shared_from_slice2", since = "1.24.0")]
 impl From<&Path> for Arc<Path> {
-    /// Converts a `Path` into an `Arc` by copying the `Path` data into a new `Arc` buffer.
+    /// Converts a [`Path`] into an [`Arc`] by copying the [`Path`] data into a new [`Arc`] buffer.
     #[inline]
     fn from(s: &Path) -> Arc<Path> {
         let arc: Arc<OsStr> = Arc::from(s.as_os_str());
@@ -1615,7 +1615,7 @@ impl From<&Path> for Arc<Path> {
 
 #[stable(feature = "shared_from_slice2", since = "1.24.0")]
 impl From<PathBuf> for Rc<Path> {
-    /// Converts a `PathBuf` into an `Rc` by moving the `PathBuf` data into a new `Rc` buffer.
+    /// Converts a [`PathBuf`] into an [`Rc`] by moving the [`PathBuf`] data into a new `Rc` buffer.
     #[inline]
     fn from(s: PathBuf) -> Rc<Path> {
         let rc: Rc<OsStr> = Rc::from(s.into_os_string());
@@ -1625,7 +1625,7 @@ impl From<PathBuf> for Rc<Path> {
 
 #[stable(feature = "shared_from_slice2", since = "1.24.0")]
 impl From<&Path> for Rc<Path> {
-    /// Converts a `Path` into an `Rc` by copying the `Path` data into a new `Rc` buffer.
+    /// Converts a [`Path`] into an [`Rc`] by copying the [`Path`] data into a new `Rc` buffer.
     #[inline]
     fn from(s: &Path) -> Rc<Path> {
         let rc: Rc<OsStr> = Rc::from(s.as_os_str());