diff --git a/acb_dirichlet/platt_c_bound.c b/acb_dirichlet/platt_c_bound.c
index ffe9e1e5..bfea8874 100644
--- a/acb_dirichlet/platt_c_bound.c
+++ b/acb_dirichlet/platt_c_bound.c
@@ -12,33 +12,6 @@
 #include "acb_dirichlet.h"
 #include "arb_hypgeom.h"
 
-/* Increase precision adaptively. */
-static void
-_gamma_upper_workaround(arb_t res, const arb_t s, const arb_t z,
-        int regularized, slong prec)
-{
-    if (!arb_is_finite(s) || !arb_is_finite(z))
-    {
-        arb_indeterminate(res);
-    }
-    else
-    {
-        arb_t x;
-        slong i;
-        arb_init(x);
-        for (i = 0; i < 5; i++)
-        {
-            arb_hypgeom_gamma_upper(x, s, z, regularized, prec << i);
-            if (arb_rel_accuracy_bits(x) > 1)
-            {
-                break;
-            }
-        }
-        arb_swap(res, x);
-        arb_clear(x);
-    }
-}
-
 static void
 _arb_pow_si(arb_t res, const arb_t x, slong y, slong prec)
 {
@@ -175,7 +148,7 @@ _pre_c_p(arb_ptr res, slong sigma, const arb_t h, ulong k, slong prec)
 
         arb_set_si(x, k + l + 1);
         arb_mul_2exp_si(x, x, -1);
-        _gamma_upper_workaround(x, x, u, 0, prec);
+        arb_hypgeom_gamma_upper(x, x, u, 0, prec);
         arb_mul(res + l, res + l, x, prec);
     }
 
diff --git a/acb_dirichlet/platt_lemma_A11.c b/acb_dirichlet/platt_lemma_A11.c
index bad7fa8b..f69009d1 100644
--- a/acb_dirichlet/platt_lemma_A11.c
+++ b/acb_dirichlet/platt_lemma_A11.c
@@ -12,33 +12,6 @@
 #include "acb_dirichlet.h"
 #include "arb_hypgeom.h"
 
-/* Increase precision adaptively. */
-static void
-_gamma_upper_workaround(arb_t res, const arb_t s, const arb_t z,
-        int regularized, slong prec)
-{
-    if (!arb_is_finite(s) || !arb_is_finite(z))
-    {
-        arb_indeterminate(res);
-    }
-    else
-    {
-        arb_t x;
-        slong i;
-        arb_init(x);
-        for (i = 0; i < 5; i++)
-        {
-            arb_hypgeom_gamma_upper(x, s, z, regularized, prec << i);
-            if (arb_rel_accuracy_bits(x) > 1)
-            {
-                break;
-            }
-        }
-        arb_swap(res, x);
-        arb_clear(x);
-    }
-}
-
 static void
 _platt_lemma_A11_X(arb_t out,
         const arb_t t0, const arb_t h, slong B, const arb_t beta, slong prec)
@@ -90,7 +63,7 @@ _platt_lemma_A11_Y(arb_t out,
     arb_sqr(x4, x4, prec);
     arb_mul_2exp_si(x4, x4, -3);
 
-    _gamma_upper_workaround(x5, x3, x4, 0, prec);
+    arb_hypgeom_gamma_upper(x5, x3, x4, 0, prec);
 
     arb_mul(out, x1, x2, prec);
     arb_mul(out, out, x5, prec);
@@ -131,7 +104,7 @@ _platt_lemma_A11_Z(arb_t out,
     arb_sqr(x4, x4, prec);
     arb_mul_2exp_si(x4, x4, -1);
 
-    _gamma_upper_workaround(x5, x3, x4, 0, prec);
+    arb_hypgeom_gamma_upper(x5, x3, x4, 0, prec);
 
     arb_mul(out, x1, x2, prec);
     arb_mul(out, out, x5, prec);
diff --git a/acb_dirichlet/platt_lemma_A5.c b/acb_dirichlet/platt_lemma_A5.c
index c8f30cf4..6e17d16c 100644
--- a/acb_dirichlet/platt_lemma_A5.c
+++ b/acb_dirichlet/platt_lemma_A5.c
@@ -12,34 +12,6 @@
 #include "acb_dirichlet.h"
 #include "arb_hypgeom.h"
 
-
-/* Increase precision adaptively. */
-static void
-_gamma_upper_workaround(arb_t res, const arb_t s, const arb_t z,
-        int regularized, slong prec)
-{
-    if (!arb_is_finite(s) || !arb_is_finite(z))
-    {
-        arb_indeterminate(res);
-    }
-    else
-    {
-        arb_t x;
-        slong i;
-        arb_init(x);
-        for (i = 0; i < 5; i++)
-        {
-            arb_hypgeom_gamma_upper(x, s, z, regularized, prec << i);
-            if (arb_rel_accuracy_bits(x) > 1)
-            {
-                break;
-            }
-        }
-        arb_swap(res, x);
-        arb_clear(x);
-    }
-}
-
 /* Lemma A5 requires B > h*sqrt(k) */
 static int
 _platt_lemma_A5_constraint(slong B, const arb_t h, slong k, slong prec)
@@ -106,7 +78,7 @@ acb_dirichlet_platt_lemma_A5(arb_t out, slong B, const arb_t h,
 
     arb_mul_2exp_si(x6, b, -1);
 
-    _gamma_upper_workaround(x6, x6, a, 0, prec);
+    arb_hypgeom_gamma_upper(x6, x6, a, 0, prec);
 
     arb_mul(out, x4, x5, prec);
     arb_mul(out, out, x6, prec);
diff --git a/acb_dirichlet/platt_ws_interpolation.c b/acb_dirichlet/platt_ws_interpolation.c
index d93aa993..be28c285 100644
--- a/acb_dirichlet/platt_ws_interpolation.c
+++ b/acb_dirichlet/platt_ws_interpolation.c
@@ -13,33 +13,6 @@
 #include "arb_hypgeom.h"
 #include "arb_poly.h"
 
-/* Increase precision adaptively. */
-static void
-_gamma_upper_workaround(arb_t res, const arb_t s, const arb_t z,
-        int regularized, slong prec)
-{
-    if (!arb_is_finite(s) || !arb_is_finite(z))
-    {
-        arb_indeterminate(res);
-    }
-    else
-    {
-        arb_t x;
-        slong i;
-        arb_init(x);
-        for (i = 0; i < 5; i++)
-        {
-            arb_hypgeom_gamma_upper(x, s, z, regularized, prec << i);
-            if (arb_rel_accuracy_bits(x) > 1)
-            {
-                break;
-            }
-        }
-        arb_swap(res, x);
-        arb_clear(x);
-    }
-}
-
 static void
 _arb_div_si_si(arb_t res, slong x, slong y, slong prec)
 {
@@ -218,7 +191,7 @@ _platt_bound_C3_Y(arb_t res, const arb_t t0, slong A, const arb_t H,
     arb_div(g2, g2, H, prec);
     arb_sqr(g2, g2, prec);
     arb_mul_2exp_si(g2, g2, -1);
-    _gamma_upper_workaround(g, g1, g2, 0, prec);
+    arb_hypgeom_gamma_upper(g, g1, g2, 0, prec);
 
     /* res = a*b*A*H*g */
     arb_mul_si(res, H, A, prec);
@@ -261,7 +234,7 @@ _platt_bound_C3_Z(arb_t res, const arb_t t0, slong A, const arb_t H,
     arb_div(g2, t0, H, prec);
     arb_sqr(g2, g2, prec);
     arb_mul_2exp_si(g2, g2, -1);
-    _gamma_upper_workaround(g, g1, g2, 0, prec);
+    arb_hypgeom_gamma_upper(g, g1, g2, 0, prec);
 
     /* res = a*b*A*g */
     arb_mul_si(res, g, A, prec);
diff --git a/acb_hypgeom/gamma_upper.c b/acb_hypgeom/gamma_upper.c
index 5f182bbd..68f3eaef 100644
--- a/acb_hypgeom/gamma_upper.c
+++ b/acb_hypgeom/gamma_upper.c
@@ -398,7 +398,9 @@ acb_hypgeom_gamma_upper(acb_t res, const acb_t s, const acb_t z, int regularized
                 c = 2.391097143;
                 ds = arf_get_d(arb_midref(acb_realref(s)), ARF_RND_DOWN);
                 dx = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN);
-                if (pow(dx - c, 8) > pow(a*ds, 8) + pow(b*prec, 8))
+                if (dx - c > a*ds + b*prec ||
+                    (dx - c > FLINT_MAX(a*ds, b*prec) &&
+                    pow(dx - c, 8) > pow(a*ds, 8) + pow(b*prec, 8)))
                 {
                     acb_hypgeom_gamma_upper_asymp(res, s, z, regularized, prec);
                     return;
diff --git a/acb_hypgeom/test/t-gamma_upper.c b/acb_hypgeom/test/t-gamma_upper.c
index 0dcbcb00..fef392b8 100644
--- a/acb_hypgeom/test/t-gamma_upper.c
+++ b/acb_hypgeom/test/t-gamma_upper.c
@@ -11,6 +11,28 @@
 
 #include "acb_hypgeom.h"
 
+
+static void
+_accuracy_regression_test(const acb_t s, const acb_t z,
+        int regularized, slong prec, slong issue, slong accuracy)
+{
+    acb_t g;
+    acb_init(g);
+    acb_hypgeom_gamma_upper(g, s, z, regularized, prec);
+    if (acb_rel_accuracy_bits(g) < accuracy)
+    {
+        flint_printf("FAIL: accuracy regression in issue #%ld\n\n", issue);
+        flint_printf("prec = %d\n\n", prec);
+        flint_printf("regularized = %d\n\n", regularized);
+        flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n");
+        flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
+        flint_printf("g = "); acb_printd(g, 30); flint_printf("\n\n");
+        flint_abort();
+    }
+    acb_clear(g);
+}
+
+
 int main()
 {
     slong iter;
@@ -211,6 +233,40 @@ int main()
         acb_clear(u);
     }
 
+    /* Accuracy regression tests. */
+    {
+        acb_t s, z;
+        slong prec, issue, accuracy;
+        acb_init(s);
+        acb_init(z);
+
+        issue = 166;
+        prec = 165;
+        accuracy = 100;
+        acb_zero(s);
+        acb_set_si(z, 110);
+        _accuracy_regression_test(s, z, 2, prec, issue, accuracy);
+
+        issue = 276;
+        prec = 300;
+        accuracy = 100;
+        acb_set_ui(s, 357);
+        acb_set_ui(z, 356);
+        _accuracy_regression_test(s, z, 0, prec, issue, accuracy);
+        arb_set_str(acb_realref(s), "356.123", prec);
+        arb_set_str(acb_realref(z), "356.456", prec);
+        _accuracy_regression_test(s, z, 0, prec, issue, accuracy);
+        arb_set_str(acb_realref(s), "357.123", prec);
+        arb_set_str(acb_realref(z), "356.456", prec);
+        _accuracy_regression_test(s, z, 0, prec, issue, accuracy);
+        arb_set_str(acb_realref(s), "357.456", prec);
+        arb_set_str(acb_realref(z), "356.123", prec);
+        _accuracy_regression_test(s, z, 0, prec, issue, accuracy);
+
+        acb_clear(s);
+        acb_clear(z);
+    }
+
     flint_randclear(state);
     flint_cleanup();
     flint_printf("PASS\n");