diff --git a/rstar/src/algorithm/nearest_neighbor.rs b/rstar/src/algorithm/nearest_neighbor.rs
index 515ed5a..cade86e 100644
--- a/rstar/src/algorithm/nearest_neighbor.rs
+++ b/rstar/src/algorithm/nearest_neighbor.rs
@@ -3,6 +3,7 @@ use crate::point::{min_inline, Point};
 use crate::{Envelope, PointDistance, RTreeObject};
 
 use alloc::{collections::BinaryHeap, vec, vec::Vec};
+use core::mem::replace;
 use heapless::binary_heap as static_heap;
 use num_traits::Bounded;
 
@@ -50,7 +51,7 @@ where
 {
     pub fn new(root: &'a ParentNode<T>, query_point: <T::Envelope as Envelope>::Point) -> Self {
         let mut result = NearestNeighborDistance2Iterator {
-            nodes: BinaryHeap::with_capacity(20),
+            nodes: SmallHeap::new(),
             query_point,
         };
         result.extend_heap(&root.children);
@@ -107,7 +108,7 @@ pub struct NearestNeighborDistance2Iterator<'a, T>
 where
     T: PointDistance + 'a,
 {
-    nodes: BinaryHeap<RTreeNodeDistanceWrapper<'a, T>>,
+    nodes: SmallHeap<RTreeNodeDistanceWrapper<'a, T>>,
     query_point: <T::Envelope as Envelope>::Point,
 }
 
@@ -161,20 +162,55 @@ impl<T: Ord> SmallHeap<T> {
         match self {
             SmallHeap::Stack(heap) => {
                 if let Err(item) = heap.push(item) {
-                    // FIXME: This could be done more efficiently if heapless'
-                    // BinaryHeap had draining, owning into_iter, or would
-                    // expose its data slice.
-                    let mut new_heap = BinaryHeap::with_capacity(heap.len() + 1);
-                    while let Some(old_item) = heap.pop() {
-                        new_heap.push(old_item);
-                    }
+                    let capacity = heap.len() + 1;
+                    let new_heap = self.spill(capacity);
                     new_heap.push(item);
-                    *self = SmallHeap::Heap(new_heap);
                 }
             }
             SmallHeap::Heap(heap) => heap.push(item),
         }
     }
+
+    pub fn extend<I>(&mut self, iter: I)
+    where
+        I: ExactSizeIterator<Item = T>,
+    {
+        match self {
+            SmallHeap::Stack(heap) => {
+                if heap.capacity() >= heap.len() + iter.len() {
+                    for item in iter {
+                        if heap.push(item).is_err() {
+                            unreachable!();
+                        }
+                    }
+                } else {
+                    let capacity = heap.len() + iter.len();
+                    let new_heap = self.spill(capacity);
+                    new_heap.extend(iter);
+                }
+            }
+            SmallHeap::Heap(heap) => heap.extend(iter),
+        }
+    }
+
+    #[cold]
+    fn spill(&mut self, capacity: usize) -> &mut BinaryHeap<T> {
+        let new_heap = BinaryHeap::with_capacity(capacity);
+        let old_heap = replace(self, SmallHeap::Heap(new_heap));
+
+        let new_heap = match self {
+            SmallHeap::Heap(new_heap) => new_heap,
+            SmallHeap::Stack(_) => unreachable!(),
+        };
+        let old_heap = match old_heap {
+            SmallHeap::Stack(old_heap) => old_heap,
+            SmallHeap::Heap(_) => unreachable!(),
+        };
+
+        new_heap.extend(old_heap.into_vec());
+
+        new_heap
+    }
 }
 
 pub fn nearest_neighbor<T>(
@@ -250,26 +286,25 @@ pub fn nearest_neighbors<T>(
 where
     T: PointDistance,
 {
-    let mut nearest_neighbors = NearestNeighborIterator::new(node, query_point.clone());
+    let mut nearest_neighbors = NearestNeighborDistance2Iterator::new(node, query_point.clone());
 
-    let first_nearest_neighbor = match nearest_neighbors.next() {
-        None => return vec![], // If we have an empty tree, just return an empty vector.
-        Some(nn) => nn,
+    let (first, first_distance_2) = match nearest_neighbors.next() {
+        Some(item) => item,
+        // If we have an empty tree, just return an empty vector.
+        None => return Vec::new(),
     };
 
     // The result will at least contain the first nearest neighbor.
-    let mut result = vec![first_nearest_neighbor];
-
-    // We compute the distance to the first nearest neighbor, and use
-    // that distance to filter out the rest of the nearest neighbors that are farther
-    // than this first neighbor.
-    let distance = first_nearest_neighbor.envelope().distance_2(&query_point);
-    nearest_neighbors
-        .take_while(|nearest_neighbor| {
-            let next_distance = nearest_neighbor.envelope().distance_2(&query_point);
-            next_distance == distance
-        })
-        .for_each(|nearest_neighbor| result.push(nearest_neighbor));
+    let mut result = vec![first];
+
+    // Use the distance to the first nearest neighbor
+    // to filter out the rest of the nearest neighbors
+    // that are farther than this first neighbor.
+    result.extend(
+        nearest_neighbors
+            .take_while(|(_, next_distance_2)| next_distance_2 == &first_distance_2)
+            .map(|(next, _)| next),
+    );
 
     result
 }