diff --git a/src/obicompactvec/src/tests/memoryvec.rs b/src/obicompactvec/src/tests/memoryvec.rs
index 21c12c9..3fd4afb 100644
--- a/src/obicompactvec/src/tests/memoryvec.rs
+++ b/src/obicompactvec/src/tests/memoryvec.rs
@@ -305,6 +305,110 @@ fn count_bits_skips_zero_words() {
     assert_eq!(count.get(127), 1);
 }
 
+// ── min / max / add / diff — overflow edge cases ──────────────────────────────
+
+#[test]
+fn miv_min_overflow_edges() {
+    // [300, 50, 400, 300] min [50, 300, 500, 200]
+    // slot 0: self=overflow(300), other=primary(50)  → 50   (overflow removed)
+    // slot 1: self=primary(50),   other=overflow(300) → 50   (no overflow created)
+    // slot 2: self=overflow(400), other=overflow(500) → 400  (overflow updated)
+    // slot 3: self=overflow(300), other=primary(200)  → 200  (overflow removed, 200 < 255)
+    let mut a = MemoryIntVec::new(4);
+    a.set(0, 300); a.set(1, 50); a.set(2, 400); a.set(3, 300);
+    let mut b = MemoryIntVec::new(4);
+    b.set(0, 50); b.set(1, 300); b.set(2, 500); b.set(3, 200);
+    IntSliceMut::min(&mut a, &b);
+    assert_eq!(a.get(0), 50);
+    assert_eq!(a.get(1), 50);
+    assert_eq!(a.get(2), 400);
+    assert_eq!(a.get(3), 200);
+    // Only slot 2 should still have an overflow entry.
+    let ov: std::collections::HashMap<usize, u32> = a.overflow_entries().collect();
+    assert_eq!(ov.len(), 1);
+    assert_eq!(ov[&2], 400);
+}
+
+#[test]
+fn miv_max_overflow_edges() {
+    // [50, 300, 100, 400] max [300, 50, 500, 200]
+    // slot 0: self=primary(50),   other=overflow(300) → 300  (overflow created)
+    // slot 1: self=overflow(300), other=primary(50)   → 300  (overflow unchanged)
+    // slot 2: self=primary(100),  other=overflow(500) → 500  (overflow created)
+    // slot 3: self=overflow(400), other=overflow(200) → 400  (overflow unchanged, 200 < 255 wait...)
+    // Wait — 200 < 255 so other slot 3 is NOT overflow. Correct: max(400, 200) = 400.
+    let mut a = MemoryIntVec::new(4);
+    a.set(0, 50); a.set(1, 300); a.set(2, 100); a.set(3, 400);
+    let mut b = MemoryIntVec::new(4);
+    b.set(0, 300); b.set(1, 50); b.set(2, 500); b.set(3, 200);
+    IntSliceMut::max(&mut a, &b);
+    assert_eq!(a.get(0), 300);
+    assert_eq!(a.get(1), 300);
+    assert_eq!(a.get(2), 500);
+    assert_eq!(a.get(3), 400);
+    let ov: std::collections::HashMap<usize, u32> = a.overflow_entries().collect();
+    assert_eq!(ov.len(), 4); // all four results >= 255
+    assert_eq!(ov[&0], 300);
+    assert_eq!(ov[&1], 300);
+    assert_eq!(ov[&2], 500);
+    assert_eq!(ov[&3], 400);
+}
+
+#[test]
+fn miv_add_overflow_edges() {
+    // [300, 50, 400, 200] + [50, 300, 200, 200]
+    // slot 0: self=overflow(300), other=primary(50)   → 350  (overflow updated)
+    // slot 1: self=primary(50),   other=overflow(300) → 350  (overflow created from primary)
+    // slot 2: self=overflow(400), other=overflow(200... wait 200 < 255)
+    //         other slot 2 is primary(200); 400+200=600 (overflow updated)
+    // slot 3: self=primary(200),  other=primary(200)  → 400  (overflow created, 400 >= 255)
+    let mut a = MemoryIntVec::new(4);
+    a.set(0, 300); a.set(1, 50); a.set(2, 400); a.set(3, 200);
+    let mut b = MemoryIntVec::new(4);
+    b.set(0, 50); b.set(1, 300); b.set(2, 200); b.set(3, 200);
+    a.add(&b);
+    assert_eq!(a.get(0), 350);
+    assert_eq!(a.get(1), 350);
+    assert_eq!(a.get(2), 600);
+    assert_eq!(a.get(3), 400);
+    let ov: std::collections::HashMap<usize, u32> = a.overflow_entries().collect();
+    assert_eq!(ov.len(), 4);
+}
+
+#[test]
+fn miv_add_both_overflow() {
+    // [300] + [400] = [700]
+    let mut a = MemoryIntVec::new(1);
+    a.set(0, 300);
+    let mut b = MemoryIntVec::new(1);
+    b.set(0, 400);
+    a.add(&b);
+    assert_eq!(a.get(0), 700);
+    let ov: std::collections::HashMap<usize, u32> = a.overflow_entries().collect();
+    assert_eq!(ov[&0], 700);
+}
+
+#[test]
+fn miv_diff_overflow_edges() {
+    // [300, 400, 400, 50] - [100, 50, 350, 300]
+    // slot 0: self=overflow(300), other=primary(100)   → 200  (overflow removed, 200 < 255)
+    // slot 1: self=overflow(400), other=primary(50)    → 350  (overflow updated, 350 >= 255)
+    // slot 2: self=overflow(400), other=overflow(350)  → 50   (overflow removed, 50 < 255)
+    // slot 3: self=primary(50),   other=overflow(300)  → 0    (saturating, stays primary)
+    let mut a = MemoryIntVec::new(4);
+    a.set(0, 300); a.set(1, 400); a.set(2, 400); a.set(3, 50);
+    let mut b = MemoryIntVec::new(4);
+    b.set(0, 100); b.set(1, 50); b.set(2, 350); b.set(3, 300);
+    a.diff(&b);
+    assert_eq!(a.get(0), 200);
+    assert_eq!(a.get(1), 350);
+    assert_eq!(a.get(2), 50);
+    assert_eq!(a.get(3), 0);
+    let ov: std::collections::HashMap<usize, u32> = a.overflow_entries().collect();
+    assert_eq!(ov.len(), 1); // only slot 1 remains overflow
+    assert_eq!(ov[&1], 350);
+}
+
 // ── Comparison operators ──────────────────────────────────────────────────────
 
 #[test]
@@ -340,6 +444,27 @@ fn cmp_leq() {
     assert!(bv.get(0)); assert!(bv.get(1)); assert!(!bv.get(2)); assert!(bv.get(3));
 }
 
+#[test]
+fn cmp_scalar_with_overflow() {
+    // Slots: [10, 1000, 50, 500, 0]
+    // geq(100): slots 1 (1000) and 3 (500) → both overflow, must qualify
+    // lt(500):  slots 0 (10), 2 (50), 4 (0) → primary; slot 1 (1000) → no; slot 3 (500) → no
+    // geq(2000): only slot 1 (1000) fails, no slot qualifies
+    let mut v = MemoryIntVec::new(5);
+    v.set(0, 10); v.set(1, 1000); v.set(2, 50); v.set(3, 500); v.set(4, 0);
+
+    let bv = v.geq(100);
+    assert!(!bv.get(0)); assert!(bv.get(1)); assert!(!bv.get(2));
+    assert!(bv.get(3)); assert!(!bv.get(4));
+
+    let bv = v.lt(500);
+    assert!(bv.get(0)); assert!(!bv.get(1)); assert!(bv.get(2));
+    assert!(!bv.get(3)); assert!(bv.get(4));
+
+    let bv = v.geq(2000);
+    assert!(!(0..5).any(|s| bv.get(s)));
+}
+
 #[test]
 fn filter_pattern() {
     // Typical filter: ingroup >= min_count AND outgroup <= max_outgroup
diff --git a/src/obicompactvec/src/traits.rs b/src/obicompactvec/src/traits.rs
index e1f15f0..0e0e903 100644
--- a/src/obicompactvec/src/traits.rs
+++ b/src/obicompactvec/src/traits.rs
@@ -1,3 +1,5 @@
+use std::collections::HashMap;
+
 use ndarray::{Array1, Array2};
 
 // ── BitSlice / BitSliceMut ────────────────────────────────────────────────────
@@ -104,8 +106,18 @@ pub trait IntSlice {
     fn cmp_scalar(&self, pred: impl Fn(u32) -> bool) -> MemoryBitVec {
         let n = self.len();
         let mut words = vec![0u64; n.div_ceil(64)];
+        let primary = self.primary_bytes();
+        // Pass 1: byte scan — no HashMap access, vectorisable for simple predicates.
+        // Overflow slots (b == 255) are left as 0 and fixed in pass 2.
         for s in 0..n {
-            if pred(self.get(s)) { words[s >> 6] |= 1u64 << (s & 63); }
+            let b = primary[s];
+            if b < 255 && pred(b as u32) {
+                words[s >> 6] |= 1u64 << (s & 63);
+            }
+        }
+        // Pass 2: fix up overflow slots — O(k), negligible.
+        for (s, val) in self.overflow_entries() {
+            if pred(val) { words[s >> 6] |= 1u64 << (s & 63); }
         }
         MemoryBitVec::from_words(words, n)
     }
@@ -146,25 +158,86 @@ pub trait IntSliceMut: IntSlice {
 
     fn min<S: IntSlice>(&mut self, other: &S) -> &mut Self {
         assert_eq!(self.len(), other.len(), "IntSlice length mismatch");
-        for s in 0..other.len() { self.set(s, self.get(s).min(other.get(s))); }
+        // Snapshot both overflow sets (O(k), tiny) before mutating self.
+        // 255 = +∞ on u8, so byte-level min is correct in all cases except
+        // both-overflow: only those slots need a fixup pass.
+        let self_ov: Vec<(usize, u32)> = self.overflow_entries().collect();
+        let other_ov: HashMap<usize, u32> = other.overflow_entries().collect();
+        self.clear_overflow();
+        // Pass 1 — SIMD-vectorizable byte min over the full primary array.
+        for (a, &b) in self.primary_bytes_mut().iter_mut().zip(other.primary_bytes()) {
+            if b < *a { *a = b; }
+        }
+        // Pass 2 — fixup slots where BOTH sides were overflow (primary = 255 after pass 1,
+        // but the overflow value may have changed).  Slots where only self was overflow are
+        // already correct: pass 1 wrote other.primary[slot] < 255 and clear_overflow removed
+        // the stale entry.
+        for (slot, self_val) in self_ov {
+            if let Some(&other_val) = other_ov.get(&slot) {
+                self.set(slot, self_val.min(other_val));
+            }
+        }
         self
     }
 
     fn max<S: IntSlice>(&mut self, other: &S) -> &mut Self {
         assert_eq!(self.len(), other.len(), "IntSlice length mismatch");
-        for s in 0..other.len() { self.set(s, self.get(s).max(other.get(s))); }
+        // Pre-pass — process other's overflow entries BEFORE the byte pass.
+        // After the byte pass, self.primary[slot] = 255 for all slots in other_ov,
+        // making it impossible to recover the original self value; we need it now.
+        for (slot, other_val) in other.overflow_entries() {
+            let self_val = self.get(slot);
+            self.set(slot, self_val.max(other_val));
+        }
+        // Pass 1 — SIMD-vectorizable byte max over the full primary array.
+        // 255 = +∞ on u8 → max(a, 255) = 255 is the correct sentinel for all
+        // overflow slots, whether handled by the pre-pass or already in self.
+        for (a, &b) in self.primary_bytes_mut().iter_mut().zip(other.primary_bytes()) {
+            if b > *a { *a = b; }
+        }
         self
     }
 
     fn add<S: IntSlice>(&mut self, other: &S) -> &mut Self {
         assert_eq!(self.len(), other.len(), "IntSlice length mismatch");
-        for s in 0..other.len() { self.set(s, self.get(s).saturating_add(other.get(s))); }
+        let n = self.len();
+        for s in 0..n {
+            // Read both primary bytes first — u8 is Copy, borrows released immediately.
+            let sb = self.primary_bytes()[s];
+            let ob = other.primary_bytes()[s];
+            if sb < 255 && ob < 255 {
+                // Hot path: no overflow lookup, no HashMap write in the common case.
+                let sum = sb as u32 + ob as u32;
+                if sum < 255 { self.primary_bytes_mut()[s] = sum as u8; }
+                else         { self.set(s, sum); }
+            } else {
+                // At least one side is in overflow — get() is unavoidable.
+                let self_val = self.get(s);
+                let other_val = other.get(s);
+                self.set(s, self_val + other_val);
+            }
+        }
         self
     }
 
     fn diff<S: IntSlice>(&mut self, other: &S) -> &mut Self {
         assert_eq!(self.len(), other.len(), "IntSlice length mismatch");
-        for s in 0..other.len() { self.set(s, self.get(s).saturating_sub(other.get(s))); }
+        let n = self.len();
+        for s in 0..n {
+            let sb = self.primary_bytes()[s];
+            let ob = other.primary_bytes()[s];
+            if sb < 255 {
+                // Result is always < 255 — no overflow created or consulted.
+                // ob == 255 means b ≥ 255 > a, so saturating result = 0.
+                self.primary_bytes_mut()[s] = if ob < 255 { sb.saturating_sub(ob) } else { 0 };
+            } else {
+                // sb == 255: self has overflow — get() unavoidable.
+                // other.get() only needed when ob == 255 too (both-overflow case).
+                let self_val = self.get(s);
+                let other_val = if ob < 255 { ob as u32 } else { other.get(s) };
+                self.set(s, self_val.saturating_sub(other_val));
+            }
+        }
         self
     }