diff --git a/src/doc/book/src/procedural-macros.md b/src/doc/book/src/procedural-macros.md
index 6c4700f9305ca..079324d56d1e6 100644
--- a/src/doc/book/src/procedural-macros.md
+++ b/src/doc/book/src/procedural-macros.md
@@ -169,7 +169,7 @@ So this is where quotes comes in. The `ast` argument is a struct that gives us
 a representation of our type (which can be either a `struct` or an `enum`).
 Check out the [docs](https://docs.rs/syn/0.10.5/syn/struct.MacroInput.html),
 there is some useful information there. We are able to get the name of the
-type using `ast.ident`. The `quote!` macro let's us write up the Rust code
+type using `ast.ident`. The `quote!` macro lets us write up the Rust code
 that we wish to return and convert it into `Tokens`. `quote!` let's us use some
 really cool templating mechanics; we simply write `#name` and `quote!` will
 replace it with the variable named `name`. You can even do some repetition
diff --git a/src/libcollections/string.rs b/src/libcollections/string.rs
index 4c82e2e2e7e35..e92eb4ff7bdd4 100644
--- a/src/libcollections/string.rs
+++ b/src/libcollections/string.rs
@@ -1250,17 +1250,17 @@ impl String {
         self.len() == 0
     }
 
-    /// Divide one string into two at an index.
+    /// Splits the string into two at the given index.
     ///
-    /// The argument, `mid`, should be a byte offset from the start of the string. It must also
-    /// be on the boundary of a UTF-8 code point.
+    /// Returns a newly allocated `String`. `self` contains bytes `[0, at)`, and
+    /// the returned `String` contains bytes `[at, len)`. `at` must be on the
+    /// boundary of a UTF-8 code point.
     ///
-    /// The two strings returned go from the start of the string to `mid`, and from `mid` to the end
-    /// of the string.
+    /// Note that the capacity of `self` does not change.
     ///
     /// # Panics
     ///
-    /// Panics if `mid` is not on a `UTF-8` code point boundary, or if it is beyond the last
+    /// Panics if `at` is not on a `UTF-8` code point boundary, or if it is beyond the last
     /// code point of the string.
     ///
     /// # Examples
@@ -1275,9 +1275,9 @@ impl String {
     /// ```
     #[inline]
     #[stable(feature = "string_split_off", since = "1.16.0")]
-    pub fn split_off(&mut self, mid: usize) -> String {
-        assert!(self.is_char_boundary(mid));
-        let other = self.vec.split_off(mid);
+    pub fn split_off(&mut self, at: usize) -> String {
+        assert!(self.is_char_boundary(at));
+        let other = self.vec.split_off(at);
         unsafe { String::from_utf8_unchecked(other) }
     }
 
diff --git a/src/libcore/iter/iterator.rs b/src/libcore/iter/iterator.rs
index d41767cce18fe..3785bbe9bb0e4 100644
--- a/src/libcore/iter/iterator.rs
+++ b/src/libcore/iter/iterator.rs
@@ -1603,12 +1603,12 @@ pub trait Iterator {
         let mut i = self.len();
 
         while let Some(v) = self.next_back() {
-            if predicate(v) {
-                return Some(i - 1);
-            }
             // No need for an overflow check here, because `ExactSizeIterator`
             // implies that the number of elements fits into a `usize`.
             i -= 1;
+            if predicate(v) {
+                return Some(i);
+            }
         }
         None
     }
diff --git a/src/libstd/env.rs b/src/libstd/env.rs
index 1ef2cb4ed153c..dd4f1ff4f5ed7 100644
--- a/src/libstd/env.rs
+++ b/src/libstd/env.rs
@@ -96,7 +96,9 @@ pub struct VarsOs { inner: os_imp::Env }
 ///
 /// While iterating, the returned iterator will panic if any key or value in the
 /// environment is not valid unicode. If this is not desired, consider using the
-/// `env::vars_os` function.
+/// [`env::vars_os`] function.
+///
+/// [`env::vars_os`]: fn.vars_os.html
 ///
 /// # Examples
 ///
@@ -171,9 +173,12 @@ impl fmt::Debug for VarsOs {
 
 /// Fetches the environment variable `key` from the current process.
 ///
-/// The returned result is `Ok(s)` if the environment variable is present and is
+/// The returned result is [`Ok(s)`] if the environment variable is present and is
 /// valid unicode. If the environment variable is not present, or it is not
-/// valid unicode, then `Err` will be returned.
+/// valid unicode, then [`Err`] will be returned.
+///
+/// [`Ok(s)`]: ../result/enum.Result.html#variant.Ok
+/// [`Err`]: ../result/enum.Result.html#variant.Err
 ///
 /// # Examples
 ///
@@ -199,7 +204,9 @@ fn _var(key: &OsStr) -> Result<String, VarError> {
 }
 
 /// Fetches the environment variable `key` from the current process, returning
-/// `None` if the variable isn't set.
+/// [`None`] if the variable isn't set.
+///
+/// [`None`]: ../option/enum.Option.html#variant.None
 ///
 /// # Examples
 ///
diff --git a/src/libstd/sync/once.rs b/src/libstd/sync/once.rs
index ba99375139139..1e7394c0b09e7 100644
--- a/src/libstd/sync/once.rs
+++ b/src/libstd/sync/once.rs
@@ -316,7 +316,7 @@ impl Once {
                         }
 
                         // Once we've enqueued ourselves, wait in a loop.
-                        // Aftewards reload the state and continue with what we
+                        // Afterwards reload the state and continue with what we
                         // were doing from before.
                         while !node.signaled.load(Ordering::SeqCst) {
                             thread::park();
diff --git a/src/libstd/thread/local.rs b/src/libstd/thread/local.rs
index 5166ddf8a21b6..66f09a7069c13 100644
--- a/src/libstd/thread/local.rs
+++ b/src/libstd/thread/local.rs
@@ -28,8 +28,8 @@ use mem;
 /// # Initialization and Destruction
 ///
 /// Initialization is dynamically performed on the first call to `with()`
-/// within a thread, and values support destructors which will be run when a
-/// thread exits.
+/// within a thread, and values that implement `Drop` get destructed when a
+/// thread exits. Some caveats apply, which are explained below.
 ///
 /// # Examples
 ///