diff --git a/src/mpn_extras/sqrhigh.c b/src/mpn_extras/sqrhigh.c
index d1578e3c5d..ece3476eae 100644
--- a/src/mpn_extras/sqrhigh.c
+++ b/src/mpn_extras/sqrhigh.c
@@ -15,6 +15,7 @@
     (at your option) any later version.  See <https://www.gnu.org/licenses/>.
 */
 
+#include <string.h>
 #include "mpn_extras.h"
 
 /* Generated by tune-sqrhigh.c */
@@ -128,25 +129,35 @@ _flint_mpn_sqrhigh_mulders_recursive(mp_ptr rp, mp_srcptr np, mp_size_t n)
     /* {rp+n-1,l+1} += 2 * {rp+l-1,l+1} */
     cy = mpn_lshift(rp + l - 1, rp + l - 1, l + 1, 1);
     cy += mpn_add_n(rp + n - 1, rp + n - 1, rp + l - 1, l + 1);
-    mpn_add_1(rp + n + l, rp + n + l, k, cy); /* propagate carry */
+    MPN_INCR_U(rp + n + l, k, cy); /* propagate carry */
+
+    /* Corrections for precise high product (not needed for the
+       original Mulders). */
+    {
+        mp_limb_t hi, lo;
+
+        /* Note: if we relax the condition on k, we will need
+           a branch for k == l here to avoid double counting. */
+        FLINT_ASSERT(k != l);
+
+        umul_ppmm(hi, lo, np[k - 1], np[l - 1]);
+        MPN_INCR_U(rp + n - 1, n + 1, hi);
+        MPN_INCR_U(rp + n - 1, n + 1, hi);
+    }
 }
 
 mp_limb_t
 _flint_mpn_sqrhigh_mulders(mp_ptr res, mp_srcptr u, mp_size_t n)
 {
-    mp_ptr tmp, tr, tu;
+    mp_ptr tmp;
     mp_limb_t bot;
     TMP_INIT;
 
     TMP_START;
-    tmp = TMP_ALLOC(sizeof(mp_limb_t) * (3 * (n + 1)));
-    tu = tmp;
-    tr = tu + (n + 1);
-    tu[0] = 0;
-    flint_mpn_copyi(tu + 1, u, n);
-    _flint_mpn_sqrhigh_mulders_recursive(tr, tu, n + 1);
-    flint_mpn_copyi(res, tr + n + 2, n);
-    bot = tr[n + 1];
+    tmp = TMP_ALLOC(sizeof(mp_limb_t) * (2 * n));
+    _flint_mpn_sqrhigh_mulders_recursive(tmp, u, n);
+    memcpy(res, tmp + n, sizeof(mp_limb_t) * n);
+    bot = tmp[n - 1];
 
     TMP_END;
     return bot;
@@ -159,7 +170,7 @@ _flint_mpn_sqrhigh_sqr(mp_ptr res, mp_srcptr u, mp_size_t n)
     mp_limb_t bot;
     tmp = flint_malloc(sizeof(mp_limb_t) * (2 * n));
     flint_mpn_sqr(tmp, u, n);
-    flint_mpn_copyi(res, tmp + n, n);
+    memcpy(res, tmp + n, sizeof(mp_limb_t) * n);
     bot = tmp[n - 1];
     flint_free(tmp);
     return bot;