diff --git a/core/src/cluster_nodes.rs b/core/src/cluster_nodes.rs
index 0445d60cdb..2d1684fb75 100644
--- a/core/src/cluster_nodes.rs
+++ b/core/src/cluster_nodes.rs
@@ -410,23 +410,11 @@ fn enable_turbine_peers_shuffle_patch(shred_slot: Slot, root_bank: &Bank) -> boo
 // Unstaked nodes will always appear at the very end.
 fn shuffle_nodes<'a, R: Rng>(rng: &mut R, nodes: &[&'a Node]) -> Vec<&'a Node> {
     // Nodes are sorted by (stake, pubkey) in descending order.
-    let stakes: Vec<u64> = nodes
-        .iter()
-        .map(|node| node.stake)
-        .take_while(|stake| *stake > 0)
-        .collect();
-    let num_staked = stakes.len();
-    let mut out: Vec<_> = WeightedShuffle::new(rng, &stakes)
+    let stakes: Vec<u64> = nodes.iter().map(|node| node.stake).collect();
+    WeightedShuffle::new(rng, &stakes)
         .unwrap()
         .map(|i| nodes[i])
-        .collect();
-    let weights = vec![1; nodes.len() - num_staked];
-    out.extend(
-        WeightedShuffle::new(rng, &weights)
-            .unwrap()
-            .map(|i| nodes[i + num_staked]),
-    );
-    out
+        .collect()
 }
 
 impl<T> ClusterNodesCache<T> {
diff --git a/gossip/src/weighted_shuffle.rs b/gossip/src/weighted_shuffle.rs
index ce6aee2c4b..3a87197c0c 100644
--- a/gossip/src/weighted_shuffle.rs
+++ b/gossip/src/weighted_shuffle.rs
@@ -26,12 +26,13 @@ pub enum WeightedShuffleError<T> {
 ///   - Returned indices are unique in the range [0, weights.len()).
 ///   - Higher weighted indices tend to appear earlier proportional to their
 ///     weight.
-///   - Zero weighted indices are excluded. Therefore the iterator may have
-///     count less than weights.len().
+///   - Zero weighted indices are shuffled and appear only at the end, after
+///     non-zero weighted indices.
 pub struct WeightedShuffle<'a, R, T> {
-    arr: Vec<T>,    // Underlying array implementing binary indexed tree.
-    sum: T,         // Current sum of weights, excluding already selected indices.
-    rng: &'a mut R, // Random number generator.
+    arr: Vec<T>,       // Underlying array implementing binary indexed tree.
+    sum: T,            // Current sum of weights, excluding already selected indices.
+    zeros: Vec<usize>, // Indices of zero weighted entries.
+    rng: &'a mut R,    // Random number generator.
 }
 
 // The implementation uses binary indexed tree:
@@ -50,12 +51,17 @@ where
         let zero = <T as Default>::default();
         let mut arr = vec![zero; size];
         let mut sum = zero;
+        let mut zeros = Vec::default();
         for (mut k, &weight) in (1usize..).zip(weights) {
             #[allow(clippy::neg_cmp_op_on_partial_ord)]
             // weight < zero does not work for NaNs.
             if !(weight >= zero) {
                 return Err(WeightedShuffleError::NegativeWeight(weight));
             }
+            if weight == zero {
+                zeros.push(k - 1);
+                continue;
+            }
             sum = sum
                 .checked_add(&weight)
                 .ok_or(WeightedShuffleError::SumOverflow)?;
@@ -64,7 +70,12 @@ where
                 k += k & k.wrapping_neg();
             }
         }
-        Ok(Self { arr, sum, rng })
+        Ok(Self {
+            arr,
+            sum,
+            rng,
+            zeros,
+        })
     }
 }
 
@@ -123,15 +134,22 @@ where
 
     fn next(&mut self) -> Option<Self::Item> {
         let zero = <T as Default>::default();
-        #[allow(clippy::neg_cmp_op_on_partial_ord)]
-        // self.sum <= zero does not work for NaNs.
-        if !(self.sum > zero) {
+        if self.sum > zero {
+            let sample =
+                <T as SampleUniform>::Sampler::sample_single(zero, self.sum, &mut self.rng);
+            let (index, weight) = WeightedShuffle::search(self, sample);
+            self.remove(index, weight);
+            return Some(index - 1);
+        }
+        if self.zeros.is_empty() {
             return None;
         }
-        let sample = <T as SampleUniform>::Sampler::sample_single(zero, self.sum, &mut self.rng);
-        let (index, weight) = WeightedShuffle::search(self, sample);
-        self.remove(index, weight);
-        Some(index - 1)
+        let index = <usize as SampleUniform>::Sampler::sample_single(
+            0usize,
+            self.zeros.len(),
+            &mut self.rng,
+        );
+        Some(self.zeros.swap_remove(index))
     }
 }
 
@@ -142,9 +160,13 @@ where
 {
     let zero = <T as Default>::default();
     let high = cumulative_weights.last().copied().unwrap_or_default();
-    #[allow(clippy::neg_cmp_op_on_partial_ord)]
-    if !(high > zero) {
-        return None;
+    if high == zero {
+        if cumulative_weights.is_empty() {
+            return None;
+        }
+        let index =
+            <usize as SampleUniform>::Sampler::sample_single(0usize, cumulative_weights.len(), rng);
+        return Some(index);
     }
     let sample = <T as SampleUniform>::Sampler::sample_single(zero, high, rng);
     let mut lo = 0usize;
@@ -234,11 +256,14 @@ mod tests {
         R: Rng,
     {
         let mut shuffle = Vec::with_capacity(weights.len());
-        loop {
-            let high: u64 = weights.iter().sum();
-            if high == 0 {
-                break shuffle;
-            }
+        let mut high: u64 = weights.iter().sum();
+        let mut zeros: Vec<_> = weights
+            .iter()
+            .enumerate()
+            .filter(|(_, w)| **w == 0)
+            .map(|(i, _)| i)
+            .collect();
+        while high != 0 {
             let sample = rng.gen_range(0, high);
             let index = weights
                 .iter()
@@ -249,8 +274,14 @@ mod tests {
                 .position(|acc| sample < acc)
                 .unwrap();
             shuffle.push(index);
+            high -= weights[index];
             weights[index] = 0;
         }
+        while !zeros.is_empty() {
+            let index = <usize as SampleUniform>::Sampler::sample_single(0usize, zeros.len(), rng);
+            shuffle.push(zeros.swap_remove(index));
+        }
+        shuffle
     }
 
     #[test]
@@ -329,14 +360,15 @@ mod tests {
         assert_eq!(weighted_sample_single(&mut rng, &weights), None);
     }
 
-    // Asserts that zero weights will return empty shuffle.
+    // Asserts that zero weights will be shuffled.
     #[test]
     fn test_weighted_shuffle_zero_weights() {
         let weights = vec![0u64; 5];
-        let mut rng = rand::thread_rng();
-        let shuffle = WeightedShuffle::new(&mut rng, &weights);
-        assert!(shuffle.unwrap().next().is_none());
-        assert_eq!(weighted_sample_single(&mut rng, &weights), None);
+        let seed = [37u8; 32];
+        let mut rng = ChaChaRng::from_seed(seed);
+        let shuffle: Vec<_> = WeightedShuffle::new(&mut rng, &weights).unwrap().collect();
+        assert_eq!(shuffle, [1, 4, 2, 3, 0]);
+        assert_eq!(weighted_sample_single(&mut rng, &weights), Some(1));
     }
 
     // Asserts that each index is selected proportional to its weight.
@@ -352,13 +384,13 @@ mod tests {
             counts[shuffle.next().unwrap()] += 1;
             let _ = shuffle.count(); // consume the rest.
         }
-        assert_eq!(counts, [101, 0, 90113, 0, 0, 891, 8895, 0]);
+        assert_eq!(counts, [95, 0, 90069, 0, 0, 908, 8928, 0]);
     }
 
     #[test]
     fn test_weighted_shuffle_hard_coded() {
         let weights = [
-            78, 70, 38, 27, 21, 0, 82, 42, 21, 77, 77, 17, 4, 50, 96, 83, 33, 16, 72,
+            78, 70, 38, 27, 21, 0, 82, 42, 21, 77, 77, 0, 17, 4, 50, 96, 0, 83, 33, 16, 72,
         ];
         let cumulative_weights: Vec<_> = weights
             .iter()
@@ -372,7 +404,7 @@ mod tests {
         let shuffle: Vec<_> = WeightedShuffle::new(&mut rng, &weights).unwrap().collect();
         assert_eq!(
             shuffle,
-            [2, 11, 16, 0, 13, 14, 15, 10, 1, 9, 7, 6, 12, 18, 4, 17, 3, 8]
+            [2, 12, 18, 0, 14, 15, 17, 10, 1, 9, 7, 6, 13, 20, 4, 19, 3, 8, 11, 16, 5]
         );
         let mut rng = ChaChaRng::from_seed(seed);
         assert_eq!(
@@ -384,12 +416,12 @@ mod tests {
         let shuffle: Vec<_> = WeightedShuffle::new(&mut rng, &weights).unwrap().collect();
         assert_eq!(
             shuffle,
-            [17, 3, 14, 13, 6, 10, 15, 16, 9, 2, 4, 1, 0, 7, 8, 18, 11, 12]
+            [19, 3, 15, 14, 6, 10, 17, 18, 9, 2, 4, 1, 0, 7, 8, 20, 12, 13, 16, 5, 11]
         );
         let mut rng = ChaChaRng::from_seed(seed);
         assert_eq!(
             weighted_sample_single(&mut rng, &cumulative_weights),
-            Some(17),
+            Some(19),
         );
     }