diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5d78a8d8ca9..71c7353174c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -21,14 +21,11 @@ You may also find the [Upgrade Guide](https://rust-random.github.io/book/update.
 - Rename `rand::distributions` to `rand::distr` (#1470)
 - The `serde1` feature has been renamed `serde` (#1477)
 - The implicit feature `rand_chacha` has been removed. This is enabled by `std_rng`. (#1473)
-- Mark `WeightError`, `PoissonError`, `BinomialError` as `#[non_exhaustive]` (#1480).
+- Mark `WeightError` as `#[non_exhaustive]` (#1480).
 - Add `p()` for `Bernoulli` to access probability (#1481)
 - Add `UniformUsize` and use to make `Uniform` for `usize` portable (#1487)
-- Remove support for generating `isize` and `usize` values with `Standard`, `Uniform` and `Fill` and usage as a `WeightedAliasIndex` weight (#1487)
 - Require `Clone` and `AsRef` bound for `SeedableRng::Seed`. (#1491)
 - Improve SmallRng initialization performance (#1482)
-- Implement `Distribution<u64>` for `Poisson<f64>` (#1498)
-- Limit the maximal acceptable lambda for `Poisson` to solve (#1312) (#1498)
 - Rename `Rng::gen_iter` to `random_iter` (#1500)
 - Rename `rand::thread_rng()` to `rand::rng()`, and remove from the prelude (#1506)
 - Remove `rand::random()` from the prelude (#1506)
diff --git a/rand_distr/CHANGELOG.md b/rand_distr/CHANGELOG.md
index c9ab729be8c..8e6cfff686b 100644
--- a/rand_distr/CHANGELOG.md
+++ b/rand_distr/CHANGELOG.md
@@ -10,6 +10,9 @@ 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)
+- Mark `WeightError`, `PoissonError`, `BinomialError` as `#[non_exhaustive]` (#1480).
+- Remove support for generating `isize` and `usize` values with `Standard`, `Uniform` and `Fill` and usage as a `WeightedAliasIndex` weight (#1487)
+- Limit the maximal acceptable lambda for `Poisson` to solve (#1312) (#1498)
 
 ### Added
 - Add plots for `rand_distr` distributions to documentation (#1434)
diff --git a/rand_distr/src/poisson.rs b/rand_distr/src/poisson.rs
index f06c29aef41..20b41ace64a 100644
--- a/rand_distr/src/poisson.rs
+++ b/rand_distr/src/poisson.rs
@@ -39,6 +39,17 @@ use rand::Rng;
 /// let v: f64 = poi.sample(&mut rand::rng());
 /// println!("{} is from a Poisson(2) distribution", v);
 /// ```
+///
+/// # Integer vs FP return type
+///
+/// This implementation uses floating-point (FP) logic internally.
+///
+/// Due to the parameter limit <code>λ < [Self::MAX_LAMBDA]</code>, it
+/// statistically impossible to sample a value larger [`u64::MAX`]. As such, it
+/// is reasonable to cast generated samples to `u64` using `as`:
+/// `distr.sample(&mut rng) as u64` (and memory safe since Rust 1.45).
+/// Similarly, when `λ < 4.2e9` it can be safely assumed that samples are less
+/// than `u32::MAX`.
 #[derive(Clone, Copy, Debug, PartialEq)]
 #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
 pub struct Poisson<F>(Method<F>)
@@ -238,14 +249,6 @@ where
     }
 }
 
-impl Distribution<u64> for Poisson<f64> {
-    #[inline]
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
-        // `as` from float to int saturates
-        <Poisson<f64> as Distribution<f64>>::sample(self, rng) as u64
-    }
-}
-
 #[cfg(test)]
 mod test {
     use super::*;
diff --git a/rand_distr/src/zeta.rs b/rand_distr/src/zeta.rs
index 3c2f55546e5..e06208c94ea 100644
--- a/rand_distr/src/zeta.rs
+++ b/rand_distr/src/zeta.rs
@@ -40,6 +40,17 @@ use rand::{distr::OpenClosed01, Rng};
 /// println!("{}", val);
 /// ```
 ///
+/// # Integer vs FP return type
+///
+/// This implementation uses floating-point (FP) logic internally, which can
+/// potentially generate very large samples (exceeding e.g. `u64::MAX`).
+///
+/// It is *safe* to cast such results to an integer type using `as`
+/// (e.g. `distr.sample(&mut rng) as u64`), since such casts are saturating
+/// (e.g. `2f64.powi(64) as u64 == u64::MAX`). It is up to the user to
+/// determine whether this potential loss of accuracy is acceptable
+/// (this determination may depend on the distribution's parameters).
+///
 /// # Notes
 ///
 /// The zeta distribution has no upper limit. Sampled values may be infinite.
diff --git a/rand_distr/src/zipf.rs b/rand_distr/src/zipf.rs
index 0a56fdf8182..9d98458db08 100644
--- a/rand_distr/src/zipf.rs
+++ b/rand_distr/src/zipf.rs
@@ -39,6 +39,13 @@ use rand::Rng;
 /// println!("{}", val);
 /// ```
 ///
+/// # Integer vs FP return type
+///
+/// This implementation uses floating-point (FP) logic internally. It may be
+/// expected that the samples are no greater than `n`, thus it is reasonable to
+/// cast generated samples to any integer type which can also represent `n`
+/// (e.g. `distr.sample(&mut rng) as u64`).
+///
 /// # Implementation details
 ///
 /// Implemented via [rejection sampling](https://en.wikipedia.org/wiki/Rejection_sampling),