diff --git a/rand_distr/src/lib.rs b/rand_distr/src/lib.rs
index 7172e8d432..1e28aaaa79 100644
--- a/rand_distr/src/lib.rs
+++ b/rand_distr/src/lib.rs
@@ -76,8 +76,9 @@
 //!   - [`UnitBall`] distribution
 //!   - [`UnitCircle`] distribution
 //!   - [`UnitDisc`] distribution
-//! - Alternative implementation for weighted index sampling
+//! - Alternative implementations for weighted index sampling
 //!   - [`WeightedAliasIndex`] distribution
+//!   - [`WeightedTreeIndex`] distribution
 //! - Misc. distributions
 //!   - [`InverseGaussian`] distribution
 //!   - [`NormalInverseGaussian`] distribution
diff --git a/rand_distr/src/weighted_tree.rs b/rand_distr/src/weighted_tree.rs
index 045c9e1f2b..2f1349126e 100644
--- a/rand_distr/src/weighted_tree.rs
+++ b/rand_distr/src/weighted_tree.rs
@@ -9,12 +9,12 @@
 //! This module contains an implementation of a tree sttructure for sampling random
 //! indices with probabilities proportional to a collection of weights.
 
-use core::ops::{Add, AddAssign, Sub, SubAssign};
+use core::ops::{Sub, SubAssign};
 
 use super::WeightedError;
 use crate::Distribution;
 use alloc::{vec, vec::Vec};
-use num_traits::Zero;
+use num_traits::{Zero, CheckedAdd};
 use rand::{distributions::uniform::SampleUniform, Rng};
 #[cfg(feature = "serde1")]
 use serde::{Deserialize, Serialize};
@@ -113,7 +113,8 @@ impl<W: Weight> WeightedTreeIndex<W> {
             } else {
                 W::zero()
             };
-            subtotals[i] = weights[i] + left_subtotal + right_subtotal;
+            let children_subtotal = left_subtotal.checked_add(&right_subtotal).ok_or(WeightedError::Overflow)?;
+            subtotals[i] = weights[i].checked_add(&children_subtotal).ok_or(WeightedError::Overflow)?;
         }
         Ok(Self { subtotals })
     }
@@ -163,11 +164,16 @@ impl<W: Weight> WeightedTreeIndex<W> {
         if weight < W::zero() {
             return Err(WeightedError::InvalidWeight);
         }
+        if let Some(total) = self.subtotals.first() {
+            if total.checked_add(&weight).is_none() {
+                return Err(WeightedError::Overflow);
+            }
+        }
         let mut index = self.len();
         self.subtotals.push(weight);
         while index != 0 {
             index = (index - 1) / 2;
-            self.subtotals[index] += weight;
+            self.subtotals[index] = self.subtotals[index].checked_add(&weight).unwrap();
         }
         Ok(())
     }
@@ -181,10 +187,15 @@ impl<W: Weight> WeightedTreeIndex<W> {
         if difference == W::zero() {
             return Ok(());
         }
-        self.subtotals[index] += difference;
+        if let Some(total) = self.subtotals.first() {
+            if total.checked_add(&difference).is_none() {
+                return Err(WeightedError::Overflow);
+            }
+        }
+        self.subtotals[index] = self.subtotals[index].checked_add(&difference).unwrap();
         while index != 0 {
             index = (index - 1) / 2;
-            self.subtotals[index] += difference;
+            self.subtotals[index] = self.subtotals[index].checked_add(&difference).unwrap();
         }
         Ok(())
     }
@@ -246,27 +257,49 @@ pub trait Weight:
     + Copy
     + SampleUniform
     + PartialOrd
-    + Add<Output = Self>
-    + AddAssign
     + Sub<Output = Self>
     + SubAssign
     + Zero
 {
+    /// Adds two numbers, checking for overflow. If overflow happens, None is returned.
+    fn checked_add(&self, b: &Self) -> Option<Self>;
 }
 
-impl<T> Weight for T where
-    T: Sized
-        + Copy
-        + SampleUniform
-        + PartialOrd
-        + Add<Output = Self>
-        + AddAssign
-        + Sub<Output = Self>
-        + SubAssign
-        + Zero
-{
+macro_rules! impl_weight_for_float {
+    ($T: ident) => {
+        impl Weight for $T {
+            fn checked_add(&self, b: &Self) -> Option<Self> {
+                Some(self + b)
+            }
+        }
+    };
 }
 
+macro_rules! impl_weight_for_int {
+    ($T: ident) => {
+        impl Weight for $T {
+            fn checked_add(&self, b: &Self) -> Option<Self> {
+                CheckedAdd::checked_add(self, b)
+            }
+        }
+    };
+}
+
+impl_weight_for_float!(f64);
+impl_weight_for_float!(f32);
+impl_weight_for_int!(usize);
+impl_weight_for_int!(u128);
+impl_weight_for_int!(u64);
+impl_weight_for_int!(u32);
+impl_weight_for_int!(u16);
+impl_weight_for_int!(u8);
+impl_weight_for_int!(isize);
+impl_weight_for_int!(i128);
+impl_weight_for_int!(i64);
+impl_weight_for_int!(i32);
+impl_weight_for_int!(i16);
+impl_weight_for_int!(i8);
+
 #[cfg(test)]
 mod test {
     use super::*;
@@ -278,6 +311,15 @@ mod test {
         assert_eq!(tree.sample(&mut rng).unwrap_err(), WeightedError::NoItem);
     }
 
+    #[test]
+    fn test_overflow_error() {
+        assert_eq!(WeightedTreeIndex::new(&[i32::MAX, 2]), Err(WeightedError::Overflow));
+        let mut tree = WeightedTreeIndex::new(&[i32::MAX - 2, 1]).unwrap();
+        assert_eq!(tree.push(3), Err(WeightedError::Overflow));
+        assert_eq!(tree.update(1, 4), Err(WeightedError::Overflow));
+        tree.update(1, 2).unwrap();
+    }
+
     #[test]
     fn test_all_weights_zero_error() {
         let tree = WeightedTreeIndex::<f64>::new(&[0.0, 0.0]).unwrap();
diff --git a/src/distributions/weighted_index.rs b/src/distributions/weighted_index.rs
index de3628b5ea..5223af594d 100644
--- a/src/distributions/weighted_index.rs
+++ b/src/distributions/weighted_index.rs
@@ -35,7 +35,9 @@ use serde::{Serialize, Deserialize};
 /// Time complexity of sampling from `WeightedIndex` is `O(log N)` where
 /// `N` is the number of weights. As an alternative,
 /// [`rand_distr::weighted_alias`](https://docs.rs/rand_distr/*/rand_distr/weighted_alias/index.html)
-/// supports `O(1)` sampling, but with much higher initialisation cost.
+/// supports `O(1)` sampling, but with much higher initialisation cost,
+/// and [`rand_distr::weighted_tree`](https://docs.rs/rand_distr/*/rand_distr/weighted_tree/index.html)
+/// supports `O(log n)` updates with O
 ///
 /// A `WeightedIndex<X>` contains a `Vec<X>` and a [`Uniform<X>`] and so its
 /// size is the sum of the size of those objects, possibly plus some alignment.