diff --git a/src/lib.rs b/src/lib.rs
index 1a45967..84b9dcc 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -38,6 +38,7 @@ where
         // construction. This allows us to copy higher layers to lower layers as construction
         // progresses, while preserving randomness in each point's layer and insertion order.
 
+        assert!(points.len() < u32::MAX as usize);
         let mut rng = SmallRng::from_entropy();
         let mut nodes = (0..points.len())
             .map(|i| (LayerId::random(&mut rng), i))
@@ -51,7 +52,7 @@ where
         let mut new_nodes = Vec::with_capacity(points.len());
         let mut out = vec![PointId::invalid(); points.len()];
         for (i, &(layer, idx)) in nodes.iter().enumerate() {
-            let pid = PointId(i);
+            let pid = PointId(i as u32);
             new_points.push(points[idx].clone());
             new_nodes.push((layer, pid));
             out[idx] = pid;
@@ -136,8 +137,6 @@ where
     /// The results are returned in the `out` parameter; the number of neighbors to search for
     /// is limited by the size of the `out` parameter, and the number of results found is returned
     /// in the return value.
-    ///
-    /// `PointId` values can be initialized with `PointId::invalid()`.
     pub fn search(&self, point: &P, out: &mut [PointId], search: &mut Search) -> usize {
         if self.points.is_empty() {
             return 0;
@@ -249,7 +248,7 @@ impl<P> Index<PointId> for Hnsw<P> {
     type Output = P;
 
     fn index(&self, index: PointId) -> &Self::Output {
-        &self.points[index.0]
+        &self.points[index.0 as usize]
     }
 }
 
@@ -257,7 +256,7 @@ impl<P: Point> Index<PointId> for Vec<P> {
     type Output = P;
 
     fn index(&self, index: PointId) -> &Self::Output {
-        &self[index.0]
+        &self[index.0 as usize]
     }
 }
 
@@ -265,7 +264,7 @@ impl<P: Point> Index<PointId> for [P] {
     type Output = P;
 
     fn index(&self, index: PointId) -> &Self::Output {
-        &self[index.0]
+        &self[index.0 as usize]
     }
 }
 
@@ -329,7 +328,7 @@ trait Layer {
                 }
             }
 
-            for pid in self.nodes()[candidate.pid.0].nearest_iter().take(num) {
+            for pid in self.nodes()[candidate.pid.0 as usize].nearest_iter().take(num) {
                 search.push(pid, point, points);
             }
         }
@@ -356,22 +355,22 @@ trait Layer {
         for (i, candidate) in found.iter().take(Self::LINKS).enumerate() {
             // `candidate` here is the new node's neighbor
             let &Candidate { distance, pid } = candidate;
-            new_nearest[i] = Some(pid); // Update the new node's `nearest`
+            new_nearest[i] = pid; // Update the new node's `nearest`
 
             let old = &points[pid];
-            let nearest = self.nodes()[pid.0].nearest();
+            let nearest = self.nodes()[pid.0 as usize].nearest();
 
             // Find the correct index to insert at to keep the neighbor's neighbors sorted
             let idx = nearest
                 .binary_search_by(|third| {
                     // `third` here is one of the neighbors of the new node's neighbor.
                     let third = match third {
-                        Some(nid) => *nid,
+                        pid if pid.is_valid() => *pid,
                         // if `third` is `None`, our new `node` is always "closer"
-                        None => return Ordering::Greater,
+                        _ => return Ordering::Greater,
                     };
 
-                    let third_distance = OrderedFloat::from(old.distance(&points[third.0]));
+                    let third_distance = OrderedFloat::from(old.distance(&points[third.0 as usize]));
                     distance.cmp(&third_distance)
                 })
                 .unwrap_or_else(|e| e);
@@ -382,15 +381,15 @@ trait Layer {
                 continue;
             }
 
-            let nearest = self.nodes_mut()[pid.0].nearest_mut();
-            if nearest[idx].is_none() {
-                nearest[idx] = Some(new);
+            let nearest = self.nodes_mut()[pid.0 as usize].nearest_mut();
+            if !nearest[idx].is_valid() {
+                nearest[idx] = new;
                 continue;
             }
 
             let end = Self::LINKS - 1;
             nearest.copy_within(idx..end, idx + 1);
-            nearest[idx] = Some(new);
+            nearest[idx] = new;
         }
 
         self.push(node);
@@ -409,15 +408,15 @@ struct UpperNode {
     /// The nearest neighbors on this layer
     ///
     /// This is always kept in sorted order (near to far).
-    nearest: [Option<PointId>; M],
+    nearest: [PointId; M],
 }
 
 impl Node for UpperNode {
-    fn nearest(&self) -> &[Option<PointId>] {
+    fn nearest(&self) -> &[PointId] {
         &self.nearest
     }
 
-    fn nearest_mut(&mut self) -> &mut [Option<PointId>] {
+    fn nearest_mut(&mut self) -> &mut [PointId] {
         &mut self.nearest
     }
 
@@ -434,15 +433,15 @@ struct ZeroNode {
     /// The nearest neighbors on this layer
     ///
     /// This is always kept in sorted order (near to far).
-    nearest: [Option<PointId>; M * 2],
+    nearest: [PointId; M * 2],
 }
 
 impl Node for ZeroNode {
-    fn nearest(&self) -> &[Option<PointId>] {
+    fn nearest(&self) -> &[PointId] {
         &self.nearest
     }
 
-    fn nearest_mut(&mut self) -> &mut [Option<PointId>] {
+    fn nearest_mut(&mut self) -> &mut [PointId] {
         &mut self.nearest
     }
 
@@ -454,13 +453,13 @@ impl Node for ZeroNode {
 }
 
 trait Node: Default {
-    fn nearest(&self) -> &[Option<PointId>];
-    fn nearest_mut(&mut self) -> &mut [Option<PointId>];
+    fn nearest(&self) -> &[PointId];
+    fn nearest_mut(&mut self) -> &mut [PointId];
     fn nearest_iter(&self) -> NearestIter<'_>;
 }
 
 struct NearestIter<'a> {
-    nearest: &'a [Option<PointId>],
+    nearest: &'a [PointId],
 }
 
 impl<'a> Iterator for NearestIter<'a> {
@@ -468,11 +467,11 @@ impl<'a> Iterator for NearestIter<'a> {
 
     fn next(&mut self) -> Option<Self::Item> {
         let (&first, rest) = self.nearest.split_first()?;
-        self.nearest = rest;
-        if first.is_none() {
-            self.nearest = &[];
+        if !first.is_valid() {
+            return None;
         }
-        first
+        self.nearest = rest;
+        Some(first)
     }
 }
 
@@ -530,11 +529,22 @@ struct Candidate {
 /// This can be used to index into the `Hnsw` to refer to the `Point` data.
 #[cfg_attr(feature = "serde", derive(Deserialize, Serialize))]
 #[derive(Clone, Copy, Debug, Eq, Hash, Ord, PartialEq, PartialOrd)]
-pub struct PointId(usize);
+pub struct PointId(u32);
 
 impl PointId {
-    pub fn invalid() -> Self {
-        PointId(usize::MAX)
+    fn invalid() -> Self {
+        PointId(u32::MAX)
+    }
+
+    /// Whether this value represents a valid point
+    pub fn is_valid(self) -> bool {
+        self.0 != u32::MAX
+    }
+}
+
+impl Default for PointId {
+    fn default() -> Self {
+        PointId::invalid()
     }
 }