diff --git a/src/libcore/ptr/mod.rs b/src/libcore/ptr/mod.rs
index 39d56958f5de0..1e051dbebcaf8 100644
--- a/src/libcore/ptr/mod.rs
+++ b/src/libcore/ptr/mod.rs
@@ -1074,17 +1074,22 @@ impl<T: ?Sized> *const T {
     /// operation because the returned value could be pointing to invalid
     /// memory.
     ///
-    /// When calling this method, you have to ensure that if the pointer is
-    /// non-NULL, then it is properly aligned, dereferencable (for the whole
-    /// size of `T`) and points to an initialized instance of `T`. This applies
-    /// even if the result of this method is unused!
+    /// When calling this method, you have to ensure that *either* the pointer is NULL *or*
+    /// all of the following is true:
+    /// - it is properly aligned
+    /// - it must point to an initialized instance of T; in particular, the pointer must be
+    ///   "dereferencable" in the sense defined [here].
+    ///
+    /// This applies even if the result of this method is unused!
     /// (The part about being initialized is not yet fully decided, but until
     /// it is, the only safe approach is to ensure that they are indeed initialized.)
     ///
     /// Additionally, the lifetime `'a` returned is arbitrarily chosen and does
-    /// not necessarily reflect the actual lifetime of the data. It is up to the
-    /// caller to ensure that for the duration of this lifetime, the memory this
-    /// pointer points to does not get written to outside of `UnsafeCell<U>`.
+    /// not necessarily reflect the actual lifetime of the data. *You* must enforce
+    /// Rust's aliasing rules. In particular, for the duration of this lifetime,
+    /// the memory the pointer points to must not get mutated (except inside `UnsafeCell`).
+    ///
+    /// [here]: crate::ptr#safety
     ///
     /// # Examples
     ///
@@ -1929,18 +1934,23 @@ impl<T: ?Sized> *mut T {
     /// of the returned pointer, nor can it ensure that the lifetime `'a`
     /// returned is indeed a valid lifetime for the contained data.
     ///
-    /// When calling this method, you have to ensure that if the pointer is
-    /// non-NULL, then it is properly aligned, dereferencable (for the whole
-    /// size of `T`) and points to an initialized instance of `T`. This applies
-    /// even if the result of this method is unused!
+    /// When calling this method, you have to ensure that *either* the pointer is NULL *or*
+    /// all of the following is true:
+    /// - it is properly aligned
+    /// - it must point to an initialized instance of T; in particular, the pointer must be
+    ///   "dereferencable" in the sense defined [here].
+    ///
+    /// This applies even if the result of this method is unused!
     /// (The part about being initialized is not yet fully decided, but until
     /// it is the only safe approach is to ensure that they are indeed initialized.)
     ///
     /// Additionally, the lifetime `'a` returned is arbitrarily chosen and does
-    /// not necessarily reflect the actual lifetime of the data. It is up to the
-    /// caller to ensure that for the duration of this lifetime, the memory this
-    /// pointer points to does not get accessed through any other pointer.
+    /// not necessarily reflect the actual lifetime of the data. *You* must enforce
+    /// Rust's aliasing rules. In particular, for the duration of this lifetime,
+    /// the memory this pointer points to must not get accessed (read or written)
+    /// through any other pointer.
     ///
+    /// [here]: crate::ptr#safety
     /// [`as_ref`]: #method.as_ref
     ///
     /// # Examples