diff --git a/hexl/ntt/inv-ntt-avx512.cpp b/hexl/ntt/inv-ntt-avx512.cpp
index a94d4e91..fd672e39 100644
--- a/hexl/ntt/inv-ntt-avx512.cpp
+++ b/hexl/ntt/inv-ntt-avx512.cpp
@@ -64,6 +64,7 @@ template void InverseTransformFromBitReverseAVX512<NTT::s_default_shift_bits>(
 template <int BitShift, bool InputLessThanMod>
 inline void InvButterfly(__m512i* X, __m512i* Y, __m512i W, __m512i W_precon,
                          __m512i neg_modulus, __m512i twice_modulus) {
+  // Compute T first to allow in-place update of X
   __m512i Y_minus_2q = _mm512_sub_epi64(*Y, twice_modulus);
   __m512i T = _mm512_sub_epi64(*X, Y_minus_2q);
 
@@ -71,6 +72,10 @@ inline void InvButterfly(__m512i* X, __m512i* Y, __m512i W, __m512i W_precon,
     // No need for modulus reduction, since inputs are in [0, q)
     *X = _mm512_add_epi64(*X, *Y);
   } else {
+    // Algorithm 3 computes (X >= 2q) ? (X - 2q) : X
+    // We instead compute (X - 2q >= 0) ? (X - 2q) : X
+    // This allows us to use the faster _mm512_movepi64_mask rather than
+    // _mm512_cmp_epu64_mask to create the mask.
     *X = _mm512_add_epi64(*X, Y_minus_2q);
     __mmask8 sign_bits = _mm512_movepi64_mask(*X);
     *X = _mm512_mask_add_epi64(*X, sign_bits, *X, twice_modulus);