diff --git a/rand_distr/CHANGELOG.md b/rand_distr/CHANGELOG.md
index c9ab729be8c..6dbb892f0e2 100644
--- a/rand_distr/CHANGELOG.md
+++ b/rand_distr/CHANGELOG.md
@@ -10,6 +10,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Move some of the computations in Binomial from `sample` to `new` (#1484)
 - Add Kolmogorov Smirnov test for sampling of `Normal` and `Binomial` (#1494)
 - Add Kolmogorov Smirnov test for more distributions (#1504)
+- Add `Distribution<u64>` support for `Zeta`, `Zipf` (#1516)
 
 ### Added
 - Add plots for `rand_distr` distributions to documentation (#1434)
diff --git a/rand_distr/src/zeta.rs b/rand_distr/src/zeta.rs
index 3c2f55546e5..ee1d420092a 100644
--- a/rand_distr/src/zeta.rs
+++ b/rand_distr/src/zeta.rs
@@ -132,6 +132,14 @@ where
     }
 }
 
+impl Distribution<u64> for Zeta<f64> {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+        // `as` from float to int saturates
+        <Zeta<f64> as Distribution<f64>>::sample(self, rng) as u64
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -163,7 +171,7 @@ mod tests {
         let d = Zeta::new(a).unwrap();
         let mut rng = crate::test::rng(1);
         for _ in 0..1000 {
-            let r = d.sample(&mut rng);
+            let r: f64 = d.sample(&mut rng);
             assert!(r >= 1.);
         }
     }
@@ -174,7 +182,7 @@ mod tests {
         let d = Zeta::new(a).unwrap();
         let mut rng = crate::test::rng(2);
         for _ in 0..1000 {
-            let r = d.sample(&mut rng);
+            let r: f64 = d.sample(&mut rng);
             assert!(r >= 1.);
         }
     }
diff --git a/rand_distr/src/zipf.rs b/rand_distr/src/zipf.rs
index 0a56fdf8182..0ee2c8c3863 100644
--- a/rand_distr/src/zipf.rs
+++ b/rand_distr/src/zipf.rs
@@ -150,6 +150,14 @@ where
     }
 }
 
+impl Distribution<u64> for Zipf<f64> {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+        // `as` from float to int saturates
+        <Zipf<f64> as Distribution<f64>>::sample(self, rng) as u64
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -186,7 +194,7 @@ mod tests {
         let d = Zipf::new(10, 0.5).unwrap();
         let mut rng = crate::test::rng(2);
         for _ in 0..1000 {
-            let r = d.sample(&mut rng);
+            let r: f64 = d.sample(&mut rng);
             assert!(r >= 1.);
         }
     }
@@ -196,7 +204,7 @@ mod tests {
         let d = Zipf::new(10, 1.).unwrap();
         let mut rng = crate::test::rng(2);
         for _ in 0..1000 {
-            let r = d.sample(&mut rng);
+            let r: f64 = d.sample(&mut rng);
             assert!(r >= 1.);
         }
     }
@@ -206,7 +214,7 @@ mod tests {
         let d = Zipf::new(10, 0.).unwrap();
         let mut rng = crate::test::rng(2);
         for _ in 0..1000 {
-            let r = d.sample(&mut rng);
+            let r: f64 = d.sample(&mut rng);
             assert!(r >= 1.);
         }
         // TODO: verify that this is a uniform distribution
@@ -217,7 +225,7 @@ mod tests {
         let d = Zipf::new(u64::MAX, 1.5).unwrap();
         let mut rng = crate::test::rng(2);
         for _ in 0..1000 {
-            let r = d.sample(&mut rng);
+            let r: f64 = d.sample(&mut rng);
             assert!(r >= 1.);
         }
         // TODO: verify that this is a zeta distribution
diff --git a/rand_distr/tests/cdf.rs b/rand_distr/tests/cdf.rs
index 8eb22740e2b..585625202d3 100644
--- a/rand_distr/tests/cdf.rs
+++ b/rand_distr/tests/cdf.rs
@@ -366,7 +366,8 @@ fn zeta() {
 
     for (seed, s) in parameters.into_iter().enumerate() {
         let dist = rand_distr::Zeta::new(s).unwrap();
-        test_discrete(seed as u64, dist, |k| cdf(k, s));
+        test_discrete::<f64, _, _>(seed as u64, dist, |k| cdf(k, s));
+        test_discrete::<u64, _, _>(seed as u64, dist, |k| cdf(k, s));
     }
 }
 
@@ -386,7 +387,8 @@ fn zipf() {
 
     for (seed, (n, x)) in parameters.into_iter().enumerate() {
         let dist = rand_distr::Zipf::new(n, x).unwrap();
-        test_discrete(seed as u64, dist, |k| cdf(k, n, x));
+        test_discrete::<f64, _, _>(seed as u64, dist, |k| cdf(k, n, x));
+        test_discrete::<u64, _, _>(seed as u64, dist, |k| cdf(k, n, x));
     }
 }