diff --git a/mpn/generic/mulhigh_n.c b/mpn/generic/mulhigh_n.c
index c74a5828..7d488b6a 100644
--- a/mpn/generic/mulhigh_n.c
+++ b/mpn/generic/mulhigh_n.c
@@ -103,7 +103,7 @@ mpn_mulshort_n_basecase (mp_ptr rp, mp_srcptr xp, mp_srcptr yp, mp_size_t n)
   mp_limb_t t1, t2, t3;
 #endif
 
-  ASSERT (n >= 3);
+  ASSERT (n >= 3);  // this restriction doesn't make a lot of sense in general
   ASSERT_MPN (xp, n);
   ASSERT_MPN (yp, n);
   ASSERT (!MPN_OVERLAP_P (rp, 2 * n, xp, n));
diff --git a/mpn/sparc32/v9/gmp-mparam.h b/mpn/sparc32/v9/gmp-mparam.h
index f5b2775a..79eba9ae 100644
--- a/mpn/sparc32/v9/gmp-mparam.h
+++ b/mpn/sparc32/v9/gmp-mparam.h
@@ -15,7 +15,7 @@
 #define MULLOW_DC_THRESHOLD              35
 #define MULLOW_MUL_THRESHOLD           9970
 
-#define MULHIGH_BASECASE_THRESHOLD        0  /* always */
+#define MULHIGH_BASECASE_THRESHOLD        3  /* always */
 #define MULHIGH_DC_THRESHOLD             34
 #define MULHIGH_MUL_THRESHOLD          9970
 
diff --git a/tune/tuneup.c b/tune/tuneup.c
index ef0ab1c8..b76642c6 100644
--- a/tune/tuneup.c
+++ b/tune/tuneup.c
@@ -918,14 +918,14 @@ tune_mulhigh (gmp_randstate_t rands)
 
   param.name = "MULHIGH_BASECASE_THRESHOLD";
   param.min_size = 3;
-  param.min_is_always = 1;
+  param.min_is_always = 3;
   //param.max_size = MULHIGH_BASECASE_THRESHOLD_LIMIT-1;
   one (&mulhigh_basecase_threshold, rands, &param);
 
   param.min_is_always = 0;	/* ??? */
 
   param.name = "MULHIGH_DC_THRESHOLD";
-  param.min_size = mulhigh_basecase_threshold;
+  param.min_size = MAX(mulhigh_basecase_threshold,4);
   param.max_size = 1000;
   one (&mulhigh_dc_threshold, rands, &param);