diff --git a/arf/set_round_mpn.c b/arf/set_round_mpn.c
index 03ba13fa..43aec13b 100644
--- a/arf/set_round_mpn.c
+++ b/arf/set_round_mpn.c
@@ -79,12 +79,10 @@ _arf_set_round_mpn(arf_t y, slong * exp_shift, mp_srcptr x, mp_size_t xn,
         }
         else if (rnd == ARF_RND_NEAR)
         {
-            bc = exp - val;
-
             /* If exactly one excess bit, there is a tie; the rounding
                direction is determined by the bit to the left of the
                truncation point. */
-            if (bc - 1 == prec)
+            if (exp - val - 1 == prec)
             {
                 increment = (x[val_limbs] >> val_bits) & 1;
             }
diff --git a/arf/test/t-mul.c b/arf/test/t-mul.c
index fbb48415..25f40ed8 100644
--- a/arf/test/t-mul.c
+++ b/arf/test/t-mul.c
@@ -28,23 +28,31 @@
 int
 arf_mul_naive(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd)
 {
-    fmpr_t a, b;
-    slong r;
+    if (rnd == ARF_RND_NEAR)
+    {
+        arf_mul(z, x, y, ARF_PREC_EXACT, rnd);
+        return arf_set_round(z, z, prec, rnd);
+    }
+    else
+    {
+        fmpr_t a, b;
+        slong r;
 
-    fmpr_init(a);
-    fmpr_init(b);
+        fmpr_init(a);
+        fmpr_init(b);
 
-    arf_get_fmpr(a, x);
-    arf_get_fmpr(b, y);
+        arf_get_fmpr(a, x);
+        arf_get_fmpr(b, y);
 
-    r = fmpr_mul_naive(a, a, b, prec, rnd);
+        r = fmpr_mul_naive(a, a, b, prec, rnd);
 
-    arf_set_fmpr(z, a);
+        arf_set_fmpr(z, a);
 
-    fmpr_clear(a);
-    fmpr_clear(b);
+        fmpr_clear(a);
+        fmpr_clear(b);
 
-    return (r == FMPR_RESULT_EXACT) ? 0 : 1;
+        return (r == FMPR_RESULT_EXACT) ? 0 : 1;
+    }
 }
 
 int main()
@@ -77,12 +85,13 @@ int main()
             if (n_randint(state, 50) == 0)
                 prec = ARF_PREC_EXACT;
 
-            switch (n_randint(state, 4))
+            switch (n_randint(state, 5))
             {
                 case 0:  rnd = ARF_RND_DOWN; break;
                 case 1:  rnd = ARF_RND_UP; break;
                 case 2:  rnd = ARF_RND_FLOOR; break;
-                default: rnd = ARF_RND_CEIL; break;
+                case 3:  rnd = ARF_RND_CEIL; break;
+                default: rnd = ARF_RND_NEAR; break;
             }
 
             switch (n_randint(state, 5))
diff --git a/arf/test/t-mul_fmpz.c b/arf/test/t-mul_fmpz.c
index a962cf58..49b8eeaa 100644
--- a/arf/test/t-mul_fmpz.c
+++ b/arf/test/t-mul_fmpz.c
@@ -68,12 +68,13 @@ int main()
             if (n_randint(state, 10))
                 prec = ARF_PREC_EXACT;
 
-            switch (n_randint(state, 4))
+            switch (n_randint(state, 5))
             {
                 case 0:  rnd = ARF_RND_DOWN; break;
                 case 1:  rnd = ARF_RND_UP; break;
                 case 2:  rnd = ARF_RND_FLOOR; break;
-                default: rnd = ARF_RND_CEIL; break;
+                case 3:  rnd = ARF_RND_CEIL; break;
+                default: rnd = ARF_RND_NEAR; break;
             }
 
             switch (n_randint(state, 2))
diff --git a/arf/test/t-mul_si.c b/arf/test/t-mul_si.c
index ef4d2589..d4056c27 100644
--- a/arf/test/t-mul_si.c
+++ b/arf/test/t-mul_si.c
@@ -68,12 +68,13 @@ int main()
             if (n_randint(state, 10) == 0)
                 prec = ARF_PREC_EXACT;
 
-            switch (n_randint(state, 4))
+            switch (n_randint(state, 5))
             {
                 case 0:  rnd = ARF_RND_DOWN; break;
                 case 1:  rnd = ARF_RND_UP; break;
                 case 2:  rnd = ARF_RND_FLOOR; break;
-                default: rnd = ARF_RND_CEIL; break;
+                case 3:  rnd = ARF_RND_CEIL; break;
+                default: rnd = ARF_RND_NEAR; break;
             }
 
             switch (n_randint(state, 2))
diff --git a/arf/test/t-mul_ui.c b/arf/test/t-mul_ui.c
index 12bf9716..c65db963 100644
--- a/arf/test/t-mul_ui.c
+++ b/arf/test/t-mul_ui.c
@@ -68,12 +68,13 @@ int main()
             if (n_randint(state, 10) == 0)
                 prec = ARF_PREC_EXACT;
 
-            switch (n_randint(state, 4))
+            switch (n_randint(state, 5))
             {
                 case 0:  rnd = ARF_RND_DOWN; break;
                 case 1:  rnd = ARF_RND_UP; break;
                 case 2:  rnd = ARF_RND_FLOOR; break;
-                default: rnd = ARF_RND_CEIL; break;
+                case 3:  rnd = ARF_RND_CEIL; break;
+                default: rnd = ARF_RND_NEAR; break;
             }
 
             switch (n_randint(state, 2))
diff --git a/arf/test/t-mul_via_mpfr.c b/arf/test/t-mul_via_mpfr.c
index b5262d63..9d2182b6 100644
--- a/arf/test/t-mul_via_mpfr.c
+++ b/arf/test/t-mul_via_mpfr.c
@@ -28,23 +28,31 @@
 int
 arf_mul_naive(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd)
 {
-    fmpr_t a, b;
-    slong r;
+    if (rnd == ARF_RND_NEAR)
+    {
+        arf_mul(z, x, y, ARF_PREC_EXACT, rnd);
+        return arf_set_round(z, z, prec, rnd);
+    }
+    else
+    {
+        fmpr_t a, b;
+        slong r;
 
-    fmpr_init(a);
-    fmpr_init(b);
+        fmpr_init(a);
+        fmpr_init(b);
 
-    arf_get_fmpr(a, x);
-    arf_get_fmpr(b, y);
+        arf_get_fmpr(a, x);
+        arf_get_fmpr(b, y);
 
-    r = fmpr_mul_naive(a, a, b, prec, rnd);
+        r = fmpr_mul_naive(a, a, b, prec, rnd);
 
-    arf_set_fmpr(z, a);
+        arf_set_fmpr(z, a);
 
-    fmpr_clear(a);
-    fmpr_clear(b);
+        fmpr_clear(a);
+        fmpr_clear(b);
 
-    return (r == FMPR_RESULT_EXACT) ? 0 : 1;
+        return (r == FMPR_RESULT_EXACT) ? 0 : 1;
+    }
 }
 
 int main()
@@ -77,12 +85,13 @@ int main()
             if (n_randint(state, 50) == 0)
                 prec = ARF_PREC_EXACT;
 
-            switch (n_randint(state, 4))
+            switch (n_randint(state, 5))
             {
                 case 0:  rnd = ARF_RND_DOWN; break;
                 case 1:  rnd = ARF_RND_UP; break;
                 case 2:  rnd = ARF_RND_FLOOR; break;
-                default: rnd = ARF_RND_CEIL; break;
+                case 3:  rnd = ARF_RND_CEIL; break;
+                default: rnd = ARF_RND_NEAR; break;
             }
 
             switch (n_randint(state, 5))
diff --git a/doc/source/arf.rst b/doc/source/arf.rst
index 8e8f752a..5f1d04ca 100644
--- a/doc/source/arf.rst
+++ b/doc/source/arf.rst
@@ -529,6 +529,7 @@ Addition and multiplication
 
     Sets `z = x \times y`, rounded to *prec* bits in the direction specified by *rnd*,
     returning nonzero iff the operation is inexact.
+    These methods support *ARF_RND_NEAR*.
 
 .. function:: int arf_add(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd)