diff --git a/mlkem/poly.c b/mlkem/poly.c
index 611f2c7d4..4ac241951 100644
--- a/mlkem/poly.c
+++ b/mlkem/poly.c
@@ -79,21 +79,23 @@ __contract__(
   ensures(return_value > -MLKEM_Q_HALF && return_value < MLKEM_Q_HALF)
 )
 {
-  /*
-   * To divide by MLKEM_Q using Barrett multiplication, the "magic number"
-   * multiplier is round_to_nearest(2**26/MLKEM_Q)
+  /* Barrett reduction approximates
+   * ```
+   *     round(a/MLKEM_Q)
+   *   = round(a*(2^N/MLKEM_Q))/2^N)
+   *  ~= round(a*round(2^N/MLKEM_Q)/2^N)
+   * ```
+   * Here, we pick N=26.
    */
-  const int BPOWER = 26;
-  const int32_t barrett_multiplier = ((1 << BPOWER) + MLKEM_Q / 2) / MLKEM_Q;
+  const int32_t magic = 20159; /* check-magic: 20159 == round(2^26 / MLKEM_Q) */
 
   /*
-   * Compute round_to_nearest(a/MLKEM_Q) using the multiplier
-   * above and shift by BPOWER places.
-   * PORTABILITY: Right-shift on a signed integer is, strictly-speaking,
-   * implementation-defined for negative left argument. Here,
-   * we assume it's sign-preserving "arithmetic" shift right. (C99 6.5.7 (5))
+   * PORTABILITY: Right-shift on a signed integer is
+   * implementation-defined for negative left argument.
+   * Here, we assume it's sign-preserving "arithmetic" shift right.
+   * See (C99 6.5.7 (5))
    */
-  const int32_t t = (barrett_multiplier * a + (1 << (BPOWER - 1))) >> BPOWER;
+  const int32_t t = (magic * a + (1 << 25)) >> 26;
 
   /*
    * t is in -10 .. +10, so we need 32-bit math to