diff --git a/test/built-ins/BigInt/constructor-integer.js b/test/built-ins/BigInt/constructor-integer.js
new file mode 100644
index 0000000000000000000000000000000000000000..36e37e60e64869716e5b5b2722edf3829ed55db0
--- /dev/null
+++ b/test/built-ins/BigInt/constructor-integer.js
@@ -0,0 +1,31 @@
+// Copyright (C) 2018 Igalia, S.L. All rights reserved.
+// This code is governed by the BSD license found in the LICENSE file.
+
+/*---
+description: BigInt constructor called with integer argument
+esid: sec-bigint-constructor
+info: |
+  BigInt ( value )
+
+  ...
+  3. If Type(prim) is Number, return ? NumberToBigInt(prim).
+
+  NumberToBigInt ( number )
+
+  ...
+  3. Return a BigInt representing the mathematical value of number.
+features: [BigInt]
+---*/
+
+assert.sameValue(BigInt(Number.MAX_SAFE_INTEGER), 9007199254740991n);
+
+assert.sameValue(BigInt(-Number.MAX_SAFE_INTEGER), -9007199254740991n);
+
+var pos = Math.pow(2, 53);
+var neg = -pos;
+
+assert.sameValue(BigInt(pos), 9007199254740992n,
+                 "BigInt(2**53) === 9007199254740992n");
+
+assert.sameValue(BigInt(neg), -9007199254740992n,
+                 "BigInt(2**53) === -9007199254740992n");
diff --git a/test/built-ins/BigInt/issafeinteger-true.js b/test/built-ins/BigInt/issafeinteger-true.js
deleted file mode 100644
index 1463edad3632b5822886a7e1ea962276a6f48ab5..0000000000000000000000000000000000000000
--- a/test/built-ins/BigInt/issafeinteger-true.js
+++ /dev/null
@@ -1,20 +0,0 @@
-// Copyright (C) 2017 Robin Templeton. All rights reserved.
-// This code is governed by the BSD license found in the LICENSE file.
-
-/*---
-description: Throws a TypeError if BigInt is called with a new target
-esid: sec-bigint-constructor
-info: |
-  ...
-  3. If Type(prim) is Number, return ? NumberToBigInt(prim).
-  ...
-
-  NumberToBigInt ( number )
-
-  2. If IsSafeInteger(number) is false, throw a RangeError exception.
-
-features: [BigInt]
----*/
-
-assert.sameValue(BigInt(Number.MAX_SAFE_INTEGER), 9007199254740991n);
-assert.sameValue(BigInt(-Number.MAX_SAFE_INTEGER), -9007199254740991n);
diff --git a/test/built-ins/BigInt/out-of-bounds-integer-rangeerror.js b/test/built-ins/BigInt/out-of-bounds-integer-rangeerror.js
deleted file mode 100644
index cae05d72bdaddd0294e3d8b8bb04c4253205b015..0000000000000000000000000000000000000000
--- a/test/built-ins/BigInt/out-of-bounds-integer-rangeerror.js
+++ /dev/null
@@ -1,40 +0,0 @@
-// Copyright (C) 2017 Robin Templeton. All rights reserved.
-// This code is governed by the BSD license found in the LICENSE file.
-
-/*---
-description: BigInt throws a RangeError if value is not a safe integer.
-esid: sec-bigint-constructor
-info: |
-  BigInt ( value )
-
-  ...
-  2. Let prim be ? ToPrimitive(value, hint Number).
-  3. If Type(prim) is Number, return ? NumberToBigInt(prim).
-  ...
-
-  NumberToBigInt ( number )
-
-  ...
-  2. If IsSafeInteger(number) is false, throw a RangeError exception.
-  ...
-
-  IsSafeInteger ( number )
-
-  ...
-  3. Let integer be ToInteger(number).
-  4. If integer is not equal to number, return false.
-  5. If abs(integer) ≤ 2**53-1, return true.
-  6. Otherwise, return false.
-features: [BigInt]
----*/
-
-var pos = Math.pow(2, 53);
-var neg = -pos;
-
-assert.throws(RangeError, function() {
-  BigInt(pos);
-});
-
-assert.throws(RangeError, function() {
-  BigInt(neg);
-});
diff --git a/test/built-ins/DataView/prototype/setBigInt64/set-values-return-undefined.js b/test/built-ins/DataView/prototype/setBigInt64/set-values-return-undefined.js
index 4e2d481c1f0a8eefd4559178f8ff853b7f25fdaa..d60507eee3be57fc8bfeae49cdab571d5554cddb 100644
--- a/test/built-ins/DataView/prototype/setBigInt64/set-values-return-undefined.js
+++ b/test/built-ins/DataView/prototype/setBigInt64/set-values-return-undefined.js
@@ -1,4 +1,4 @@
-// Copyright (C) 2017 Igalia, S.L. All rights reserved.
+// Copyright (C) 2018 Igalia, S.L. All rights reserved.
 // This code is governed by the BSD license found in the LICENSE file.
 
 /*---
@@ -20,7 +20,7 @@ values.forEach(function(value, i) {
       () => sample.setBigInt64(0, BigInt(value), false),
       "value: " + value);
     return;
-  } else if (!Number.isInteger(value) || value > 9007199254740991) {
+  } else if (!Number.isInteger(value)) {
     assert.throws(RangeError,
       () => sample.setBigInt64(0, BigInt(value), false),
       "value " + value);