diff --git a/crypto/fipsmodule/ec/asm/p256-x86_64-asm.pl b/crypto/fipsmodule/ec/asm/p256-x86_64-asm.pl
index 6a021dbcf..994cb82d5 100755
--- a/crypto/fipsmodule/ec/asm/p256-x86_64-asm.pl
+++ b/crypto/fipsmodule/ec/asm/p256-x86_64-asm.pl
@@ -3112,17 +3112,24 @@ $code.=<<___;
 
 	or	$acc5, $acc4			# see if result is zero
 	or	$acc0, $acc4
-	or	$acc1, $acc4
+	or	$acc1, $acc4			# !is_equal(U1, U2)
 
-	.byte	0x3e				# predict taken
-	jnz	.Ladd_proceed$x			# is_equal(U1,U2)?
 	movq	%xmm2, $acc0
 	movq	%xmm3, $acc1
-	test	$acc0, $acc0
-	jnz	.Ladd_proceed$x			# (in1infty || in2infty)?
-	test	$acc1, $acc1
-	jz	.Ladd_double$x			# is_equal(S1,S2)?
+	or	$acc0, $acc4
+	.byte	0x3e				# predict taken
+	jnz	.Ladd_proceed$x			# !is_equal(U1, U2) || in1infty || in2infty
 
+	# We now know A = B or A = -B and neither is infinity. Compare the
+	# y-coordinates via S1 and S2.
+	test	$acc1, $acc1
+	jz	.Ladd_double$x			# is_equal(S1, S2)
+
+	# A = -B, so the result is infinity.
+	#
+	# TODO(davidben): Does .Ladd_proceed handle this case? It seems to, in
+	# which case we should eliminate this special-case and simplify the
+	# timing analysis.
 	movq	%xmm0, $r_ptr			# restore $r_ptr
 	pxor	%xmm0, %xmm0
 	movdqu	%xmm0, 0x00($r_ptr)
diff --git a/crypto/fipsmodule/ec/ec_montgomery.c b/crypto/fipsmodule/ec/ec_montgomery.c
index 6fb32c477..0cf1d910d 100644
--- a/crypto/fipsmodule/ec/ec_montgomery.c
+++ b/crypto/fipsmodule/ec/ec_montgomery.c
@@ -282,7 +282,8 @@ void ec_GFp_mont_add(const EC_GROUP *group, EC_RAW_POINT *out,
   BN_ULONG yneq = ec_felem_non_zero_mask(group, &r);
 
   // This case will never occur in the constant-time |ec_GFp_mont_mul|.
-  if (!xneq && !yneq && z1nz && z2nz) {
+  BN_ULONG is_nontrivial_double = ~xneq & ~yneq & z1nz & z2nz;
+  if (is_nontrivial_double) {
     ec_GFp_mont_dbl(group, out, a);
     return;
   }
diff --git a/crypto/fipsmodule/ec/p224-64.c b/crypto/fipsmodule/ec/p224-64.c
index cc88f15f6..f8af39bef 100644
--- a/crypto/fipsmodule/ec/p224-64.c
+++ b/crypto/fipsmodule/ec/p224-64.c
@@ -758,7 +758,9 @@ static void p224_point_add(p224_felem x3, p224_felem y3, p224_felem z3,
   z1_is_zero = p224_felem_is_zero(z1);
   z2_is_zero = p224_felem_is_zero(z2);
   // In affine coordinates, (X_1, Y_1) == (X_2, Y_2)
-  if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
+  p224_limb is_nontrivial_double =
+      x_equal & y_equal & (1 - z1_is_zero) & (1 - z2_is_zero);
+  if (is_nontrivial_double) {
     p224_point_double(x3, y3, z3, x1, y1, z1);
     return;
   }
diff --git a/third_party/fiat/p256.c b/third_party/fiat/p256.c
index 8426beb3c..23ec71f98 100644
--- a/third_party/fiat/p256.c
+++ b/third_party/fiat/p256.c
@@ -321,7 +321,10 @@ static void point_add(fe x3, fe y3, fe z3, const fe x1,
 
   limb_t yneq = fe_nz(r);
 
-  if (!xneq && !yneq && z1nz && z2nz) {
+  limb_t is_nontrivial_double = constant_time_is_zero_w(xneq | yneq) &
+                                ~constant_time_is_zero_w(z1nz) &
+                                ~constant_time_is_zero_w(z2nz);
+  if (is_nontrivial_double) {
     point_double(x3, y3, z3, x1, y1, z1);
     return;
   }