diff --git a/library/alloc/src/collections/vec_deque/mod.rs b/library/alloc/src/collections/vec_deque/mod.rs
index 86d77182bccee..858069903af0d 100644
--- a/library/alloc/src/collections/vec_deque/mod.rs
+++ b/library/alloc/src/collections/vec_deque/mod.rs
@@ -531,12 +531,13 @@ impl<T> VecDeque<T> {
     ///
     /// let deque: VecDeque<u32> = VecDeque::new();
     /// ```
-    // FIXME: This should probably be const
     #[inline]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_stable(feature = "const_vec_deque_new", since = "CURRENT_RUSTC_VERSION")]
     #[must_use]
-    pub fn new() -> VecDeque<T> {
-        VecDeque::new_in(Global)
+    pub const fn new() -> VecDeque<T> {
+        // FIXME: This should just be `VecDeque::new_in(Global)` once that's stable.
+        VecDeque { head: 0, len: 0, buf: RawVec::NEW }
     }
 
     /// Creates an empty deque with space for at least `capacity` elements.
@@ -566,10 +567,9 @@ impl<T, A: Allocator> VecDeque<T, A> {
     ///
     /// let deque: VecDeque<u32> = VecDeque::new();
     /// ```
-    // FIXME: This should probably be const
     #[inline]
     #[unstable(feature = "allocator_api", issue = "32838")]
-    pub fn new_in(alloc: A) -> VecDeque<T, A> {
+    pub const fn new_in(alloc: A) -> VecDeque<T, A> {
         VecDeque { head: 0, len: 0, buf: RawVec::new_in(alloc) }
     }
 
@@ -2152,7 +2152,7 @@ impl<T, A: Allocator> VecDeque<T, A> {
 
             self.head = tail;
         } else {
-            // ´free` is smaller than both `head_len` and `tail_len`.
+            // `free` is smaller than both `head_len` and `tail_len`.
             // the general algorithm for this first moves the slices
             // right next to each other and then uses `slice::rotate`
             // to rotate them into place:
@@ -2789,9 +2789,9 @@ impl<T, A: Allocator> From<Vec<T, A>> for VecDeque<T, A> {
     /// [`Vec<T>`]: crate::vec::Vec
     /// [`VecDeque<T>`]: crate::collections::VecDeque
     ///
-    /// In its current implementation, this is a very cheap
-    /// conversion. This isn't yet a guarantee though, and
-    /// shouldn't be relied on.
+    /// This conversion is guaranteed to run in *O*(1) time
+    /// and to not re-allocate the `Vec`'s buffer or
+    /// allocate any additional memory.
     fn from(other: Vec<T, A>) -> Self {
         let (ptr, len, cap, alloc) = other.into_raw_parts_with_alloc();
         Self { head: 0, len, buf: unsafe { RawVec::from_raw_parts_in(ptr, cap, alloc) } }