diff --git a/libnail/src/align/mod.rs b/libnail/src/align/mod.rs
index d95325e..bfa2937 100644
--- a/libnail/src/align/mod.rs
+++ b/libnail/src/align/mod.rs
@@ -17,7 +17,8 @@ pub use optimal_accuracy::optimal_accuracy;
 
 mod scoring;
 pub use scoring::{
-    cloud_score, e_value, null_one_score, null_two_score, p_value, Bits, Nats, Score,
+    cloud_score, e_value, null_one_score, null_two_score, p_value, Bits, Nats, NullTwoScratch,
+    Score,
 };
 
 mod traceback;
diff --git a/libnail/src/align/scoring.rs b/libnail/src/align/scoring.rs
index e71cc75..e02c52e 100644
--- a/libnail/src/align/scoring.rs
+++ b/libnail/src/align/scoring.rs
@@ -217,18 +217,52 @@ pub fn null_one_score(target_length: usize) -> Nats {
     Nats(target_length as f32 * p_null_loop.ln() + p_null_exit.ln())
 }
 
+/// Reusable scratch buffers for `null_two_score`. Allocate once per thread via
+/// `NullTwoScratch::default()` and pass `&mut scratch` on every call to avoid
+/// per-call heap allocation.
+#[derive(Default, Clone)]
+pub struct NullTwoScratch {
+    pub expected_prob_ratios: Vec<f32>,
+    pub match_sums: Vec<f32>,
+    pub insert_sums: Vec<f32>,
+    pub core_posteriors: Vec<f32>,
+}
+
+impl NullTwoScratch {
+    fn prepare(&mut self, profile_length: usize, target_length: usize) {
+        // Grow each buffer if the current call needs more capacity than we've
+        // seen before; otherwise reuse the existing allocation.  Either way,
+        // zero only the prefix that this call will actually read/write —
+        // leaving stale values beyond the active range is intentional.
+        Self::zero_prefix(&mut self.expected_prob_ratios, Profile::MAX_DEGENERATE_ALPHABET_SIZE);
+        Self::zero_prefix(&mut self.match_sums, profile_length + 1);
+        Self::zero_prefix(&mut self.insert_sums, profile_length + 1);
+        Self::zero_prefix(&mut self.core_posteriors, target_length + 1);
+    }
+
+    #[inline]
+    fn zero_prefix(v: &mut Vec<f32>, n: usize) {
+        if v.len() < n {
+            v.resize(n, 0.0); // allocates only when a new high-water mark is reached
+        } else {
+            v[..n].fill(0.0); // only touches the n elements this call will use
+        }
+    }
+}
+
 /// Compute the null two score adjustment: the composition bias.
 pub fn null_two_score(
     posterior_matrix: &impl DpMatrix,
     profile: &Profile,
     target: &Sequence,
     row_bounds: &RowBounds,
+    scratch: &mut NullTwoScratch,
 ) -> Nats {
-    // TODO: prevent these allocations?
-    let mut expected_prob_ratios: Vec<f32> = vec![0.0; Profile::MAX_DEGENERATE_ALPHABET_SIZE];
-    let mut match_sums: Vec<f32> = vec![0.0; profile.length + 1];
-    let mut insert_sums: Vec<f32> = vec![0.0; profile.length + 1];
-    let mut core_posteriors: Vec<f32> = vec![0.0; target.length + 1];
+    scratch.prepare(profile.length, target.length);
+    let expected_prob_ratios = &mut scratch.expected_prob_ratios;
+    let match_sums = &mut scratch.match_sums;
+    let insert_sums = &mut scratch.insert_sums;
+    let core_posteriors = &mut scratch.core_posteriors;
     let mut core_state_sum: f32 = 0.0;
 
     // what: for each position in the model, take the sum of
diff --git a/nail/src/pipeline/align_stage.rs b/nail/src/pipeline/align_stage.rs
index 01c7478..b2732c9 100644
--- a/nail/src/pipeline/align_stage.rs
+++ b/nail/src/pipeline/align_stage.rs
@@ -6,7 +6,7 @@ use libnail::{
     align::{
         backward, forward, null_one_score, null_two_score, optimal_accuracy, p_value, posterior,
         structs::{Alignment, AlignmentBuilder, DpMatrixSparse, RowBounds, Trace},
-        traceback, Bits,
+        traceback, Bits, NullTwoScratch,
     },
     structs::{Profile, Sequence},
 };
@@ -72,6 +72,7 @@ pub struct DefaultAlignStage {
     backward_matrix: DpMatrixSparse,
     posterior_matrix: DpMatrixSparse,
     optimal_matrix: DpMatrixSparse,
+    null_two_scratch: NullTwoScratch,
     forward_p_value_threshold: f64,
     target_count: usize,
     config: AlignConfig,
@@ -184,6 +185,7 @@ impl AlignStage for DefaultAlignStage {
                 profile,
                 target,
                 bounds,
+                &mut self.null_two_scratch,
             ));
             stats.null_two_time(now.elapsed());
             score
diff --git a/nail/src/stats.rs b/nail/src/stats.rs
index 5aba9cc..29ec6e1 100644
--- a/nail/src/stats.rs
+++ b/nail/src/stats.rs
@@ -97,6 +97,7 @@ pub enum ThreadedTimed {
     Forward,
     Backward,
     Posterior,
+    OptimalAccuracy,
     Traceback,
     NullTwo,
     OutputWrite,
@@ -115,6 +116,7 @@ impl Debug for ThreadedTimed {
             ThreadedTimed::Forward => "forward",
             ThreadedTimed::Backward => "backward",
             ThreadedTimed::Posterior => "posterior",
+            ThreadedTimed::OptimalAccuracy => "optimal accuracy",
             ThreadedTimed::Traceback => "traceback",
             ThreadedTimed::NullTwo => "null two",
         };
@@ -264,6 +266,7 @@ impl Stats {
 
                         self.add_threaded_time(ThreadedTimed::Backward, stats.backward_time);
                         self.add_threaded_time(ThreadedTimed::Posterior, stats.posterior_time);
+                        self.add_threaded_time(ThreadedTimed::OptimalAccuracy, stats.optimal_accuracy_time);
                         self.add_threaded_time(ThreadedTimed::Traceback, stats.traceback_time);
                         self.add_threaded_time(ThreadedTimed::NullTwo, stats.null_two_time);
                     }