diff --git a/src/iter.rs b/src/iter.rs
index 4c26a8f..fb54567 100644
--- a/src/iter.rs
+++ b/src/iter.rs
@@ -31,11 +31,11 @@ pub trait NonEmptyIterator {
 
     /// Each `NonEmptyIterator` knows about a possibly-empty variant of itself,
     /// likely from `std`. Critically, they share an `Item`.
-    type Iter: Iterator<Item = Self::Item>;
+    type IntoIter: IntoIterator<Item = Self::Item>;
 
     /// A `NonEmptyIterator` can, by consuming itself, reliably produce its
     /// first element, alongside its possibly-empty variant.
-    fn first(self) -> (Self::Item, Self::Iter);
+    fn first(self) -> (Self::Item, Self::IntoIter);
 
     /// Advances the iterator and returns the next value.
     ///
@@ -201,7 +201,17 @@ pub trait NonEmptyIterator {
         // Differs from the implementation of `Iterator::count` to absolutely
         // ensure that `count` returns at least 1.
         let (_, rest) = self.first();
-        1 + rest.count()
+        1 + rest.into_iter().count()
+    }
+
+    /// Repeats a non-empty iterator endlessly.
+    ///
+    /// See also [`Iterator::cycle`].
+    fn cycle(self) -> Cycle<Self>
+    where
+        Self: Sized + Clone,
+    {
+        Cycle::new(self)
     }
 
     /// Creates a non-empty iterator which gives the current iteration count as
@@ -450,14 +460,14 @@ where
 {
     type Item = U;
 
-    type Iter = std::iter::Map<I::Iter, F>;
+    type IntoIter = std::iter::Map<<I::IntoIter as IntoIterator>::IntoIter, F>;
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         let (i, iter) = self.iter.first();
         let mut fun = self.f;
 
         // Reconstruct the `Map` we broke open.
-        (fun(i), iter.map(fun))
+        (fun(i), iter.into_iter().map(fun))
     }
 
     fn next(&mut self) -> Option<Self::Item> {
@@ -498,12 +508,12 @@ where
 {
     type Item = T;
 
-    type Iter = std::iter::Cloned<I::Iter>;
+    type IntoIter = std::iter::Cloned<<I::IntoIter as IntoIterator>::IntoIter>;
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         let (i, iter) = self.iter.first();
 
-        (i.clone(), iter.cloned())
+        (i.clone(), iter.into_iter().cloned())
     }
 
     fn next(&mut self) -> Option<Self::Item> {
@@ -539,12 +549,12 @@ where
 {
     type Item = (usize, I::Item);
 
-    type Iter = std::iter::Enumerate<I::Iter>;
+    type IntoIter = std::iter::Enumerate<<I::IntoIter as IntoIterator>::IntoIter>;
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         let (head, rest) = self.iter.first();
 
-        ((0, head), rest.enumerate())
+        ((0, head), rest.into_iter().enumerate())
     }
 
     fn next(&mut self) -> Option<Self::Item> {
@@ -582,15 +592,15 @@ where
 {
     type Item = I::Item;
 
-    type Iter = std::iter::Take<I::Iter>;
+    type IntoIter = std::iter::Take<<I::IntoIter as IntoIterator>::IntoIter>;
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         let (head, rest) = self.iter.first();
 
         if self.n < 2 {
-            (head, rest.take(0))
+            (head, rest.into_iter().take(0))
         } else {
-            (head, rest.take(self.n - 1))
+            (head, rest.into_iter().take(self.n - 1))
         }
     }
 
@@ -630,12 +640,12 @@ where
 {
     type Item = A::Item;
 
-    type Iter = std::iter::Chain<A::Iter, B>;
+    type IntoIter = std::iter::Chain<<A::IntoIter as IntoIterator>::IntoIter, B>;
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         let (head, a_rest) = self.a.first();
 
-        (head, a_rest.chain(self.b))
+        (head, a_rest.into_iter().chain(self.b))
     }
 
     fn next(&mut self) -> Option<Self::Item> {
@@ -676,9 +686,9 @@ where
 {
     type Item = T;
 
-    type Iter = std::option::IntoIter<T>;
+    type IntoIter = std::option::IntoIter<T>;
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         (self.once, None.into_iter())
     }
 
@@ -718,12 +728,12 @@ where
 {
     type Item = T;
 
-    type Iter = std::iter::Copied<I::Iter>;
+    type IntoIter = std::iter::Copied<<I::IntoIter as IntoIterator>::IntoIter>;
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         let (head, rest) = self.iter.first();
 
-        (head.clone(), rest.copied())
+        (head.clone(), rest.into_iter().copied())
     }
 
     fn next(&mut self) -> Option<Self::Item> {
@@ -744,3 +754,52 @@ where
         self.iter.into_iter().copied()
     }
 }
+
+/// An iterator that repeats endlessly.
+///
+/// See also [`std::iter::Cycle`].
+pub struct Cycle<I> {
+    orig: I,
+    iter: I,
+}
+
+impl<I: Clone> Cycle<I> {
+    fn new(iter: I) -> Self {
+        Self {
+            orig: iter.clone(),
+            iter,
+        }
+    }
+}
+
+impl<I, T> NonEmptyIterator for Cycle<I>
+where
+    I: NonEmptyIterator<Item = T>,
+    Self: IntoIterator<Item = T>,
+{
+    type Item = T;
+
+    type IntoIter = Self;
+
+    fn first(self) -> (Self::Item, Self::IntoIter) {
+        todo!()
+    }
+
+    fn next(&mut self) -> Option<Self::Item> {
+        todo!()
+    }
+}
+
+impl<I, J, T> IntoIterator for Cycle<I>
+where
+    I: IntoIterator<Item = T, IntoIter = J>,
+    J: Clone + Iterator<Item = T>,
+{
+    type Item = T;
+
+    type IntoIter = std::iter::Cycle<I::IntoIter>;
+
+    fn into_iter(self) -> Self::IntoIter {
+        todo!()
+    }
+}
diff --git a/src/set.rs b/src/set.rs
index a6e0a92..d0c5551 100644
--- a/src/set.rs
+++ b/src/set.rs
@@ -464,9 +464,9 @@ impl<'a, T> IntoIterator for &'a NESet<T> {
 impl<'a, T> NonEmptyIterator for Iter<'a, T> {
     type Item = &'a T;
 
-    type Iter = Skip<Chain<Once<&'a T>, std::collections::hash_set::Iter<'a, T>>>;
+    type IntoIter = Skip<Chain<Once<&'a T>, std::collections::hash_set::Iter<'a, T>>>;
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         (self.head, self.iter.skip(1))
     }
 
@@ -513,7 +513,7 @@ where
 {
     type Item = &'a T;
 
-    type Iter = std::collections::hash_set::Union<'a, T, S>;
+    type IntoIter = std::collections::hash_set::Union<'a, T, S>;
 
     fn next(&mut self) -> Option<Self::Item> {
         match self.orig_iter.next() {
@@ -527,7 +527,7 @@ where
         }
     }
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         (&self.orig.head, self.orig.tail.union(&self.other.tail))
     }
 
diff --git a/src/vector.rs b/src/vector.rs
index 3c92a58..06d25b8 100644
--- a/src/vector.rs
+++ b/src/vector.rs
@@ -822,13 +822,13 @@ pub struct Iter<'a, T: 'a> {
 
 impl<'a, T> NonEmptyIterator for Iter<'a, T> {
     type Item = &'a T;
-    type Iter = Skip<Chain<Once<&'a T>, std::slice::Iter<'a, T>>>;
+    type IntoIter = Skip<Chain<Once<&'a T>, std::slice::Iter<'a, T>>>;
 
     fn next(&mut self) -> Option<Self::Item> {
         self.iter.next()
     }
 
-    fn first(self) -> (Self::Item, Self::Iter) {
+    fn first(self) -> (Self::Item, Self::IntoIter) {
         (self.head, self.iter.skip(1))
     }
 }