diff --git a/src/cartesian_power.rs b/src/cartesian_power.rs
new file mode 100644
index 000000000..3cf3562ab
--- /dev/null
+++ b/src/cartesian_power.rs
@@ -0,0 +1,356 @@
+use alloc::vec::Vec;
+use std::fmt;
+use std::iter::FusedIterator;
+
+/// An adaptor iterating through all the ordered `n`-length lists of items
+/// yielded by the underlying iterator, including repetitions.
+///
+/// See [`.cartesian_power()`](crate::Itertools::cartesian_power)
+/// for more information.
+#[derive(Clone)]
+#[must_use = "iterator adaptors are lazy and do nothing unless consumed"]
+pub struct CartesianPower<I>
+where
+    I: Iterator,
+    I::Item: Clone,
+{
+    pow: usize,
+    iter: Option<I>,     // Inner iterator. Forget once consumed after 'base' iterations.
+    items: Vec<I::Item>, // Fill from iter. Clear once adaptor is exhausted. Final length is 'base'.
+    indices: Vec<usize>, // Indices just yielded. Clear once adaptor is exhausted. Length is 'pow'.
+}
+
+/// Create a new `CartesianPower` from an iterator of clonables.
+pub fn cartesian_power<I>(iter: I, pow: usize) -> CartesianPower<I>
+where
+    I: Iterator,
+    I::Item: Clone,
+{
+    CartesianPower {
+        pow,
+        iter: Some(iter),
+        items: Vec::new(),
+        indices: Vec::new(),
+    }
+}
+
+impl<I> CartesianPower<I>
+where
+    I: Iterator,
+    I::Item: Clone,
+{
+    /// Increments internal indices to advance to the next list to be yielded.
+    /// This collects new items from the underlying iterator
+    /// if they were not all already collected.
+    ///
+    /// Returns None if we've run out of possible lists,
+    /// otherwise return refs to the indices to yield next,
+    /// valid within the collected items slice also returned.
+    fn increment_indices(&mut self) -> Option<(&[usize], &[I::Item])> {
+        let Self {
+            pow,
+            iter,
+            items,
+            indices,
+        } = self;
+        match (*pow, iter, items.len()) {
+            // Final stable state: underlying iterator and items forgotten.
+            (_, None, 0) => None,
+
+            // Degenerated 0th power iteration.
+            (0, Some(_), _) => {
+                self.iter = None; // Forget without even consuming.
+                Some((indices, items))
+            }
+
+            (pow, Some(it), 0) => {
+                // Check whether there is at least one element in the iterator.
+                if let Some(first) = it.next() {
+                    // Allocate buffer to hold items about to be yielded.
+                    items.reserve_exact(it.size_hint().0);
+                    items.push(first);
+                    // Same for indices to be yielded.
+                    indices.reserve_exact(pow);
+                    for _ in 0..pow {
+                        indices.push(0);
+                    }
+                    return Some((indices, items));
+                }
+                // Degenerated iteration over an empty set, yet with non-null power.
+                self.iter = None;
+                None
+            }
+
+            (pow, Some(it), base) => {
+                // We are still unsure whether all items have been collected.
+                // As a consequence, 'base' is still uncertain,
+                // but then we know that indices haven't started wrapping around yet.
+                if let Some(next) = it.next() {
+                    items.push(next);
+                    indices[pow - 1] += 1;
+                    return Some((indices, items));
+                }
+
+                // All items have just been collected.
+                self.iter = None;
+                if base == 1 || pow == 1 {
+                    // End of iteration.
+                    items.clear();
+                    indices.clear();
+                    return None;
+                }
+
+                // First wrap around.
+                indices[pow - 1] = 0;
+                indices[pow - 2] += 1;
+                Some((indices, items))
+            }
+
+            (_, None, b) => {
+                // Keep yielding items list, incrementing indices rightmost first.
+                for index in indices.iter_mut().rev() {
+                    *index += 1;
+                    if *index < b {
+                        return Some((indices, items));
+                    }
+                    *index = 0; // Wrap and increment left.
+                }
+                items.clear();
+                indices.clear();
+                None
+            }
+        }
+    }
+
+    /// Same as [`increment_indices`], but does n increments at once.
+    fn increment_indices_by_n(&mut self, n: usize) -> Option<(&[usize], &[I::Item])> {
+        todo!()
+    }
+}
+
+impl<I> Iterator for CartesianPower<I>
+where
+    I: Iterator,
+    I::Item: Clone,
+{
+    type Item = Vec<I::Item>;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        // If anything to yield,
+        // clone the correct 'pow' instances of collected items
+        // into a freshly allocated vector.
+        self.increment_indices().map(|(indices, items)| {
+            indices
+                .iter()
+                .map(|&i| items[i].clone())
+                .collect::<Vec<_>>()
+        })
+    }
+
+    fn nth(&mut self, n: usize) -> Option<Self::Item> {
+        self.increment_indices_by_n(n).map(|(indices, items)| {
+            indices
+                .iter()
+                .map(|&i| items[i].clone())
+                .collect::<Vec<_>>()
+        })
+    }
+
+    fn size_hint(&self) -> (usize, Option<usize>) {
+        todo!()
+    }
+
+    fn count(self) -> usize {
+        todo!()
+    }
+}
+
+// Elide underlying iterator from the debug display.
+impl<I> fmt::Debug for CartesianPower<I>
+where
+    I: Iterator + fmt::Debug,
+    I::Item: fmt::Debug + Clone,
+{
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        let Self {
+            pow,
+            iter,
+            items,
+            indices,
+        } = self;
+        f.debug_struct("CartesianPower")
+            .field("pow", pow)
+            .field("iter", &iter.is_some())
+            .field("items", items)
+            .field("indices", indices)
+            .finish()
+    }
+}
+
+impl<I> FusedIterator for CartesianPower<I>
+where
+    I: Iterator,
+    I::Item: Clone,
+{
+}
+
+#[cfg(test)]
+mod tests {
+    //! Use chars and string to ease testing of every yielded iterator values.
+
+    use super::CartesianPower;
+    use crate::Itertools;
+    use core::str::Chars;
+
+    fn check_fused(mut exhausted_it: CartesianPower<Chars>, context: String) {
+        for i in 0..100 {
+            let act = exhausted_it.next();
+            assert!(
+                act.is_none(),
+                "Iteration {} after expected exhaustion of {} \
+                yielded {:?} instead of None. ",
+                i,
+                context,
+                act,
+            );
+        }
+    }
+
+    #[test]
+    fn basic() {
+        fn check(origin: &str, pow: usize, expected: &[&str]) {
+            let mut it = origin.chars().cartesian_power(pow);
+            let mut i = 0;
+            for exp in expected {
+                let act = it.next();
+                if act != Some(exp.chars().collect()) {
+                    panic!(
+                        "Failed iteration {} for {:?}^{}. \
+                         Expected {:?}, got {:?} instead.",
+                        i, origin, pow, exp, act,
+                    );
+                }
+                i += 1;
+            }
+            check_fused(it, format!("iteration {} or {:?}^{}", i, origin, pow));
+        }
+
+        // Empty underlying iterator.
+        check("", 0, &[""]);
+        check("", 1, &[]);
+        check("", 2, &[]);
+        check("", 3, &[]);
+
+        // Singleton underlying iterator.
+        check("a", 0, &[""]);
+        check("a", 1, &["a"]);
+        check("a", 2, &["aa"]);
+        check("a", 3, &["aaa"]);
+
+        // Underlying pair.
+        check("ab", 0, &[""]);
+        check("ab", 1, &["a", "b"]);
+        check("ab", 2, &["aa", "ab", "ba", "bb"]);
+        check(
+            "ab",
+            3,
+            &["aaa", "aab", "aba", "abb", "baa", "bab", "bba", "bbb"],
+        );
+
+        // Underlying triplet.
+        check("abc", 0, &[""]);
+        check("abc", 1, &["a", "b", "c"]);
+        check(
+            "abc",
+            2,
+            &["aa", "ab", "ac", "ba", "bb", "bc", "ca", "cb", "cc"],
+        );
+        check(
+            "abc",
+            3,
+            &[
+                "aaa", "aab", "aac", "aba", "abb", "abc", "aca", "acb", "acc", "baa", "bab", "bac",
+                "bba", "bbb", "bbc", "bca", "bcb", "bcc", "caa", "cab", "cac", "cba", "cbb", "cbc",
+                "cca", "ccb", "ccc",
+            ],
+        );
+    }
+
+    #[test]
+    fn nth() {
+        fn check(origin: &str, pow: usize, expected: &[(usize, Option<&str>)]) {
+            let mut it = origin.chars().cartesian_power(pow);
+            let mut total_n = Vec::new();
+            for &(n, exp) in expected {
+                let act = it.nth(n);
+                total_n.push(n);
+                if act != exp.map(|s| s.chars().collect::<Vec<_>>()) {
+                    panic!(
+                        "Failed nth({}) iteration for {:?}^{}. \
+                         Expected {:?}, got {:?} instead.",
+                        total_n
+                            .iter()
+                            .map(ToString::to_string)
+                            .collect::<Vec<_>>()
+                            .join(", "),
+                        origin,
+                        pow,
+                        exp,
+                        act,
+                    );
+                }
+            }
+            check_fused(
+                it,
+                format!(
+                    "nth({}) iteration of {:?}^{}",
+                    total_n
+                        .iter()
+                        .map(ToString::to_string)
+                        .collect::<Vec<_>>()
+                        .join(", "),
+                    origin,
+                    pow
+                ),
+            );
+        }
+
+        // HERE: make it work with the new implementation.
+
+        // Check degenerated cases.
+        check("", 0, &[(0, Some("")), (0, None)]);
+        check("", 0, &[(0, Some("")), (1, None)]);
+        check("", 0, &[(0, Some("")), (2, None)]);
+        check("", 0, &[(1, None), (0, None)]);
+        check("", 0, &[(1, None), (1, None)]);
+        check("", 0, &[(1, None), (2, None)]);
+        check("", 0, &[(2, None), (0, None)]);
+        check("", 0, &[(2, None), (1, None)]);
+        check("", 0, &[(2, None), (2, None)]);
+
+        check("a", 0, &[(0, Some("")), (0, None)]);
+        check("a", 0, &[(0, Some("")), (1, None)]);
+        check("a", 0, &[(0, Some("")), (2, None)]);
+        check("a", 0, &[(1, None), (0, None)]);
+        check("a", 0, &[(1, None), (1, None)]);
+        check("a", 0, &[(1, None), (2, None)]);
+        check("a", 0, &[(2, None), (0, None)]);
+        check("a", 0, &[(2, None), (1, None)]);
+        check("a", 0, &[(2, None), (2, None)]);
+
+        // Unit power.
+        check("a", 1, &[(0, Some("a")), (0, None)]);
+        check("a", 1, &[(0, Some("a")), (1, None)]);
+        check("a", 1, &[(0, Some("a")), (2, None)]);
+        check("a", 1, &[(1, None), (0, None)]);
+        check("a", 1, &[(1, None), (1, None)]);
+        check("a", 1, &[(1, None), (2, None)]);
+        check("a", 1, &[(2, None), (0, None)]);
+        check("a", 1, &[(2, None), (1, None)]);
+        check("a", 1, &[(2, None), (2, None)]);
+
+        check("ab", 1, &[(0, Some("a")), (0, Some("b")), (0, None)]);
+        check("ab", 1, &[(1, Some("b")), (0, None), (0, None)]);
+        check("ab", 1, &[(2, None), (0, None), (0, None)]);
+    }
+}
diff --git a/src/lib.rs b/src/lib.rs
index f4de79c50..aed13b4a4 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -57,6 +57,7 @@ extern crate alloc;
 #[cfg(feature = "use_alloc")]
 use alloc::{collections::VecDeque, string::String, vec::Vec};
 
+use cartesian_power::CartesianPower;
 pub use either::Either;
 
 use core::borrow::Borrow;
@@ -175,6 +176,8 @@ pub mod free;
 #[doc(inline)]
 pub use crate::free::*;
 #[cfg(feature = "use_alloc")]
+mod cartesian_power;
+#[cfg(feature = "use_alloc")]
 mod combinations;
 #[cfg(feature = "use_alloc")]
 mod combinations_with_replacement;
@@ -1729,6 +1732,23 @@ pub trait Itertools: Iterator {
         combinations_with_replacement::combinations_with_replacement(self, k)
     }
 
+    /// Returns an iterator yielding the successive elements
+    /// of the cartesian power of the set described by the original iterator.
+    ///
+    /// ```
+    /// use itertools::Itertools;
+    ///
+    /// TODO: illustrative example.
+    /// ```
+    #[cfg(feature = "use_alloc")]
+    fn cartesian_power(self, pow: usize) -> CartesianPower<Self>
+    where
+        Self: Sized,
+        Self::Item: Clone,
+    {
+        cartesian_power::cartesian_power(self, pow)
+    }
+
     /// Return an iterator adaptor that iterates over all k-permutations of the
     /// elements from an iterator.
     ///