diff --git a/src/liballoc/collections/btree/map.rs b/src/liballoc/collections/btree/map.rs
index bf5748739d47..d2f4278d0d0e 100644
--- a/src/liballoc/collections/btree/map.rs
+++ b/src/liballoc/collections/btree/map.rs
@@ -47,9 +47,9 @@
 /// any other key, as determined by the [`Ord`] trait, changes while it is in the map. This is
 /// normally only possible through [`Cell`], [`RefCell`], global state, I/O, or unsafe code.
 ///
-/// [`Ord`]: ../../std/cmp/trait.Ord.html
-/// [`Cell`]: ../../std/cell/struct.Cell.html
-/// [`RefCell`]: ../../std/cell/struct.RefCell.html
+/// [`Ord`]: core::cmp::Ord
+/// [`Cell`]: core::cell::Cell
+/// [`RefCell`]: core::cell::RefCell
 ///
 /// # Examples
 ///
@@ -256,8 +256,7 @@ fn replace(&mut self, key: K) -> Option<K> {
 /// This `struct` is created by the [`iter`] method on [`BTreeMap`]. See its
 /// documentation for more.
 ///
-/// [`iter`]: struct.BTreeMap.html#method.iter
-/// [`BTreeMap`]: struct.BTreeMap.html
+/// [`iter`]: BTreeMap::iter
 #[stable(feature = "rust1", since = "1.0.0")]
 pub struct Iter<'a, K: 'a, V: 'a> {
     range: Range<'a, K, V>,
@@ -276,8 +275,7 @@ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
 /// This `struct` is created by the [`iter_mut`] method on [`BTreeMap`]. See its
 /// documentation for more.
 ///
-/// [`iter_mut`]: struct.BTreeMap.html#method.iter_mut
-/// [`BTreeMap`]: struct.BTreeMap.html
+/// [`iter_mut`]: BTreeMap::iter_mut
 #[stable(feature = "rust1", since = "1.0.0")]
 #[derive(Debug)]
 pub struct IterMut<'a, K: 'a, V: 'a> {
@@ -290,8 +288,7 @@ pub struct IterMut<'a, K: 'a, V: 'a> {
 /// This `struct` is created by the [`into_iter`] method on [`BTreeMap`]
 /// (provided by the `IntoIterator` trait). See its documentation for more.
 ///
-/// [`into_iter`]: struct.BTreeMap.html#method.into_iter
-/// [`BTreeMap`]: struct.BTreeMap.html
+/// [`into_iter`]: IntoIterator::into_iter
 #[stable(feature = "rust1", since = "1.0.0")]
 pub struct IntoIter<K, V> {
     front: Option<Handle<NodeRef<marker::Owned, K, V, marker::Leaf>, marker::Edge>>,
@@ -315,8 +312,7 @@ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
 /// This `struct` is created by the [`keys`] method on [`BTreeMap`]. See its
 /// documentation for more.
 ///
-/// [`keys`]: struct.BTreeMap.html#method.keys
-/// [`BTreeMap`]: struct.BTreeMap.html
+/// [`keys`]: BTreeMap::keys
 #[stable(feature = "rust1", since = "1.0.0")]
 pub struct Keys<'a, K: 'a, V: 'a> {
     inner: Iter<'a, K, V>,
@@ -334,8 +330,7 @@ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
 /// This `struct` is created by the [`values`] method on [`BTreeMap`]. See its
 /// documentation for more.
 ///
-/// [`values`]: struct.BTreeMap.html#method.values
-/// [`BTreeMap`]: struct.BTreeMap.html
+/// [`values`]: BTreeMap::values
 #[stable(feature = "rust1", since = "1.0.0")]
 pub struct Values<'a, K: 'a, V: 'a> {
     inner: Iter<'a, K, V>,
@@ -353,8 +348,7 @@ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
 /// This `struct` is created by the [`values_mut`] method on [`BTreeMap`]. See its
 /// documentation for more.
 ///
-/// [`values_mut`]: struct.BTreeMap.html#method.values_mut
-/// [`BTreeMap`]: struct.BTreeMap.html
+/// [`values_mut`]: BTreeMap::values_mut
 #[stable(feature = "map_values_mut", since = "1.10.0")]
 #[derive(Debug)]
 pub struct ValuesMut<'a, K: 'a, V: 'a> {
@@ -366,8 +360,7 @@ pub struct ValuesMut<'a, K: 'a, V: 'a> {
 /// This `struct` is created by the [`range`] method on [`BTreeMap`]. See its
 /// documentation for more.
 ///
-/// [`range`]: struct.BTreeMap.html#method.range
-/// [`BTreeMap`]: struct.BTreeMap.html
+/// [`range`]: BTreeMap::range
 #[stable(feature = "btree_range", since = "1.17.0")]
 pub struct Range<'a, K: 'a, V: 'a> {
     front: Option<Handle<NodeRef<marker::Immut<'a>, K, V, marker::Leaf>, marker::Edge>>,
@@ -386,8 +379,7 @@ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
 /// This `struct` is created by the [`range_mut`] method on [`BTreeMap`]. See its
 /// documentation for more.
 ///
-/// [`range_mut`]: struct.BTreeMap.html#method.range_mut
-/// [`BTreeMap`]: struct.BTreeMap.html
+/// [`range_mut`]: BTreeMap::range_mut
 #[stable(feature = "btree_range", since = "1.17.0")]
 pub struct RangeMut<'a, K: 'a, V: 'a> {
     front: Option<Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge>>,
@@ -412,8 +404,7 @@ fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
 ///
 /// This `enum` is constructed from the [`entry`] method on [`BTreeMap`].
 ///
-/// [`BTreeMap`]: struct.BTreeMap.html
-/// [`entry`]: struct.BTreeMap.html#method.entry
+/// [`entry`]: BTreeMap::entry
 #[stable(feature = "rust1", since = "1.0.0")]
 pub enum Entry<'a, K: 'a, V: 'a> {
     /// A vacant entry.