diff --git a/mp_div.c b/mp_div.c
index cbc52e8..b092d7b 100644
--- a/mp_div.c
+++ b/mp_div.c
@@ -26,7 +26,7 @@ mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
    }
 
    if (MP_HAS(S_MP_DIV_RECURSIVE)
-       && (b->used > MP_MUL_KARATSUBA_CUTOFF)
+       && (b->used > (2 * MP_MUL_KARATSUBA_CUTOFF))
        && (b->used <= ((a->used/3)*2))) {
       err = s_mp_div_recursive(a, b, c, d);
    } else if (MP_HAS(S_MP_DIV_SCHOOL)) {
diff --git a/s_mp_div_recursive.c b/s_mp_div_recursive.c
index df9a297..d719c4e 100644
--- a/s_mp_div_recursive.c
+++ b/s_mp_div_recursive.c
@@ -20,7 +20,7 @@ static mp_err s_recursion(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
    mp_int A1, A2, B1, B0, Q1, Q0, R1, R0, t;
    int m = a->used - b->used, k = m/2;
 
-   if (m < MP_MUL_KARATSUBA_CUTOFF) {
+   if (m < (MP_MUL_KARATSUBA_CUTOFF)) {
       return s_mp_div_school(a, b, q, r);
    }
 
@@ -43,15 +43,16 @@ static mp_err s_recursion(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
    if ((err = mp_sub(&A1, &t, &A1)) != MP_OKAY)                            goto LBL_ERR;
 
    /* while A1 < 0 do Q1 = Q1 - 1, A1 = A1 + (beta^k * B) */
-   if ((err = mp_mul_2d(b, k * MP_DIGIT_BIT, &t)) != MP_OKAY)              goto LBL_ERR;
-   while (mp_cmp_d(&A1, 0uL) == MP_LT) {
-      if ((err = mp_decr(&Q1)) != MP_OKAY)                                 goto LBL_ERR;
-      if ((err = mp_add(&A1, &t, &A1)) != MP_OKAY)                         goto LBL_ERR;
+   if (mp_cmp_d(&A1, 0uL) == MP_LT) {
+      if ((err = mp_mul_2d(b, k * MP_DIGIT_BIT, &t)) != MP_OKAY)           goto LBL_ERR;
+      do {
+         if ((err = mp_decr(&Q1)) != MP_OKAY)                              goto LBL_ERR;
+         if ((err = mp_add(&A1, &t, &A1)) != MP_OKAY)                      goto LBL_ERR;
+      } while (mp_cmp_d(&A1, 0uL) == MP_LT);
    }
-
    /* (Q0, R0) =  RecursiveDivRem(A1 / beta^(k), B1) */
    if ((err = mp_div_2d(&A1, k * MP_DIGIT_BIT, &A1, &t)) != MP_OKAY)       goto LBL_ERR;
-   if ((err = s_recursion(&A1, &B1, &Q0, &R0)) != MP_OKAY)              goto LBL_ERR;
+   if ((err = s_recursion(&A1, &B1, &Q0, &R0)) != MP_OKAY)                 goto LBL_ERR;
 
    /* A2 = (R0*beta^k) +  (A1 % beta^k) - (Q0*B0) */
    if ((err = mp_lshd(&R0, k)) != MP_OKAY)                                 goto LBL_ERR;
@@ -65,13 +66,10 @@ static mp_err s_recursion(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
       if ((err = mp_add(&A2, b, &A2)) != MP_OKAY)                          goto LBL_ERR;
    }
    /* return q = (Q1*beta^k) + Q0, r = A2 */
-   if (q != NULL) {
-      if ((err = mp_lshd(&Q1, k)) != MP_OKAY)                              goto LBL_ERR;
-      if ((err = mp_add(&Q1, &Q0, q)) != MP_OKAY)                          goto LBL_ERR;
-   }
-   if (r != NULL) {
-      if ((err = mp_copy(&A2, r)) != MP_OKAY)                              goto LBL_ERR;
-   }
+   if ((err = mp_lshd(&Q1, k)) != MP_OKAY)                                 goto LBL_ERR;
+   if ((err = mp_add(&Q1, &Q0, q)) != MP_OKAY)                             goto LBL_ERR;
+
+   if ((err = mp_copy(&A2, r)) != MP_OKAY)                                 goto LBL_ERR;
 
 LBL_ERR:
    mp_clear_multi(&A1, &A2, &B1, &B0, &Q1, &Q0, &R1, &R0, &t, NULL);
@@ -94,24 +92,7 @@ mp_err s_mp_div_recursive(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
    /* most significant bit of a limb */
    /* assumes  MP_DIGIT_MAX < (sizeof(mp_digit) * CHAR_BIT) */
    msb = (MP_DIGIT_MAX + (mp_digit)(1)) >> 1;
-
-   /*
-       Method to compute sigma shamelessly stolen from
-
-       J. Burnikel and J. Ziegler, "Fast recursive division", Research Report
-       MPI-I-98-1-022, Max-Planck-Institut fuer Informatik, Saarbruecken, Germany,
-       October 1998. (available online)
-
-       Vid. section 2.3.
-    */
-   m = MP_MUL_KARATSUBA_CUTOFF;
-   while (m <= b->used) {
-      m <<= 1;
-   }
-   j = (b->used + m - 1) / m;
-   n = j * m;
-
-   sigma = MP_DIGIT_BIT * (n - b->used);
+   sigma = 0;
    msb_b = b->dp[b->used - 1];
    while (msb_b < msb) {
       sigma++;
@@ -139,7 +120,7 @@ mp_err s_mp_div_recursive(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
    /* Q = 0 */
    mp_zero(&Q);
    while (m > n) {
-      /* (q, r) = RecursveDivRem(A / (beta^(m-n)), B) */
+      /* (q, r) = RecursiveDivRem(A / (beta^(m-n)), B) */
       j = (m - n) * MP_DIGIT_BIT;
       if ((err = mp_div_2d(&A, j, &A_div, &A_mod)) != MP_OKAY)                   goto LBL_ERR;
       if ((err = s_recursion(&A_div, &B, &Q1, &R)) != MP_OKAY)                goto LBL_ERR;
@@ -152,7 +133,7 @@ mp_err s_mp_div_recursive(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r
       /* m = m - n */
       m = m - n;
    }
-   /* (q, r) = RecursveDivRem(A, B) */
+   /* (q, r) = RecursiveDivRem(A, B) */
    if ((err = s_recursion(&A, &B, &Q1, &R)) != MP_OKAY)                       goto LBL_ERR;
    /* Q = (Q * beta^m) + q, R = r */
    if ((err = mp_mul_2d(&Q, m * MP_DIGIT_BIT, &Q)) != MP_OKAY)                   goto LBL_ERR;