diff --git a/lib/test.js b/lib/test.js
index e1dbb8a6..bf3cbd8a 100644
--- a/lib/test.js
+++ b/lib/test.js
@@ -432,7 +432,6 @@ function equal(a, b, msg, extra) {
 Test.prototype.equal
 = Test.prototype.equals
 = Test.prototype.isEqual
-= Test.prototype.is
 = equal;
 
 function strictEqual(a, b, msg, extra) {
@@ -449,13 +448,14 @@ function strictEqual(a, b, msg, extra) {
 }
 Test.prototype.strictEqual
 = Test.prototype.strictEquals
+= Test.prototype.is
 = strictEqual;
 
 function notEqual(a, b, msg, extra) {
     if (arguments.length < 2) {
         throw new TypeError('two arguments must be provided to compare');
     }
-    this._assert(a !== b, {
+    this._assert(a != b, {
         message: defined(msg, 'should not be equal'),
         operator: 'notEqual',
         actual: a,
@@ -465,15 +465,29 @@ function notEqual(a, b, msg, extra) {
 }
 Test.prototype.notEqual
 = Test.prototype.notEquals
-= Test.prototype.notStrictEqual
-= Test.prototype.notStrictEquals
 = Test.prototype.isNotEqual
-= Test.prototype.isNot
-= Test.prototype.not
 = Test.prototype.doesNotEqual
 = Test.prototype.isInequal
 = notEqual;
 
+function notStrictEqual(a, b, msg, extra) {
+    if (arguments.length < 2) {
+        throw new TypeError('two arguments must be provided to compare');
+    }
+    this._assert(!is(a, b), {
+        message: defined(msg, 'should not be strictly equal'),
+        operator: 'notStrictEqual',
+        actual: a,
+        expected: b,
+        extra: extra
+    });
+}
+Test.prototype.notStrictEqual
+= Test.prototype.notStrictEquals
+= Test.prototype.isNot
+= Test.prototype.not
+= notStrictEqual;
+
 function tapeDeepEqual(a, b, msg, extra) {
     if (arguments.length < 2) {
         throw new TypeError('two arguments must be provided to compare');
diff --git a/readme.markdown b/readme.markdown
index d62e64b0..756eeba1 100644
--- a/readme.markdown
+++ b/readme.markdown
@@ -217,17 +217,27 @@ Aliases: `t.ifError()`, `t.ifErr()`, `t.iferror()`
 
 ## t.equal(actual, expected, msg)
 
-Assert that `actual === expected` with an optional description of the assertion `msg`.
+Assert that `actual == expected` with an optional description of the assertion `msg`.
 
-Aliases: `t.equals()`, `t.isEqual()`, `t.is()`, `t.strictEqual()`,
-`t.strictEquals()`
+Aliases: `t.equals()`, `t.isEqual()`
+
+## t.strictEqual(actual, expected, msg)
+
+Assert that `Object.is(actual, expected)` with an optional description of the assertion `msg`.
+
+Aliases: `t.is()`, `t.strictEqual()`, `t.strictEquals()`
 
 ## t.notEqual(actual, expected, msg)
 
-Assert that `actual !== expected` with an optional description of the assertion `msg`.
+Assert that `actual != expected` with an optional description of the assertion `msg`.
+
+Aliases: `t.notEquals()`, `t.isNotEqual()`, `t.doesNotEqual()`, `t.isInequal()`
+
+## t.notStrictEqual(actual, expected, msg)
+
+Assert that `!Object.is(actual, expected)` with an optional description of the assertion `msg`.
 
-Aliases: `t.notEquals()`, `t.notStrictEqual()`, `t.notStrictEquals()`,
-`t.isNotEqual()`, `t.isNot()`, `t.not()`, `t.doesNotEqual()`, `t.isInequal()`
+Aliases: `t.notStrictEqual()`, `t.notStrictEquals()`, `t.isNot()`, `t.not()`
 
 ## t.deepEqual(actual, expected, msg)
 
diff --git a/test/edge-cases.js b/test/edge-cases.js
index 5840ad63..00b0072c 100644
--- a/test/edge-cases.js
+++ b/test/edge-cases.js
@@ -17,7 +17,35 @@ tap.test('edge cases', function (tt) {
             + '# zeroes\n'
             + 'ok 1 0 equal to -0\n'
             + 'ok 2 -0 equal to 0\n'
-            + 'not ok 3 0 strictEqual to -0\n'
+            + 'not ok 3 0 notEqual to -0\n'
+            + '  ---\n'
+            + '    operator: notEqual\n'
+            + '    expected: |-\n'
+            + '      -0\n'
+            + '    actual: |-\n'
+            + '      0\n'
+            + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: 0 notEqual to -0\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 4 -0 notEqual to 0\n'
+            + '  ---\n'
+            + '    operator: notEqual\n'
+            + '    expected: |-\n'
+            + '      0\n'
+            + '    actual: |-\n'
+            + '      -0\n'
+            + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: -0 notEqual to 0\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 5 0 strictEqual to -0\n'
             + '  ---\n'
             + '    operator: strictEqual\n'
             + '    expected: |-\n'
@@ -31,7 +59,7 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 4 -0 strictEqual to 0\n'
+            + 'not ok 6 -0 strictEqual to 0\n'
             + '  ---\n'
             + '    operator: strictEqual\n'
             + '    expected: |-\n'
@@ -45,9 +73,39 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 5 0 deepLooseEqual to -0\n'
-            + 'ok 6 -0 deepLooseEqual to 0\n'
-            + 'not ok 7 0 deepEqual to -0\n'
+            + 'ok 7 0 notStrictEqual to -0\n'
+            + 'ok 8 -0 notStrictEqual to 0\n'
+            + 'ok 9 0 deepLooseEqual to -0\n'
+            + 'ok 10 -0 deepLooseEqual to 0\n'
+            + 'not ok 11 0 notDeepLooseEqual to -0\n'
+            + '  ---\n'
+            + '    operator: notDeepLooseEqual\n'
+            + '    expected: |-\n'
+            + '      -0\n'
+            + '    actual: |-\n'
+            + '      0\n'
+            + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: 0 notDeepLooseEqual to -0\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 12 -0 notDeepLooseEqual to 0\n'
+            + '  ---\n'
+            + '    operator: notDeepLooseEqual\n'
+            + '    expected: |-\n'
+            + '      0\n'
+            + '    actual: |-\n'
+            + '      -0\n'
+            + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: -0 notDeepLooseEqual to 0\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 13 0 deepEqual to -0\n'
             + '  ---\n'
             + '    operator: deepEqual\n'
             + '    expected: |-\n'
@@ -61,7 +119,7 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 8 -0 deepEqual to 0\n'
+            + 'not ok 14 -0 deepEqual to 0\n'
             + '  ---\n'
             + '    operator: deepEqual\n'
             + '    expected: |-\n'
@@ -75,8 +133,10 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
+            + 'ok 15 0 notDeepEqual to -0\n'
+            + 'ok 16 -0 notDeepEqual to 0\n'
             + '# NaNs\n'
-            + 'not ok 9 NaN equal to NaN\n'
+            + 'not ok 17 NaN equal to NaN\n'
             + '  ---\n'
             + '    operator: equal\n'
             + '    expected: NaN\n'
@@ -88,8 +148,21 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 10 NaN strictEqual to NaN\n'
-            + 'not ok 11 NaN deepLooseEqual to NaN\n'
+            + 'ok 18 NaN notEqual to NaN\n'
+            + 'ok 19 NaN strictEqual to NaN\n'
+            + 'not ok 20 NaN notStrictEqual to NaN\n'
+            + '  ---\n'
+            + '    operator: notStrictEqual\n'
+            + '    expected: NaN\n'
+            + '    actual:   NaN\n'
+            + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: NaN notStrictEqual to NaN\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 21 NaN deepLooseEqual to NaN\n'
             + '  ---\n'
             + '    operator: deepLooseEqual\n'
             + '    expected: NaN\n'
@@ -101,38 +174,63 @@ tap.test('edge cases', function (tt) {
             + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 12 NaN deepEqual to NaN\n'
-            + '\n1..12\n'
-            + '# tests 12\n'
-            + '# pass  6\n'
-            + '# fail  6\n'
+            + 'ok 22 NaN notDeepLooseEqual to NaN\n'
+            + 'ok 23 NaN deepEqual to NaN\n'
+            + 'not ok 24 NaN notDeepEqual to NaN\n'
+            + '  ---\n'
+            + '    operator: notDeepEqual\n'
+            + '    expected: NaN\n'
+            + '    actual:   NaN\n'
+            + '    at: Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: NaN notDeepEqual to NaN\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/edge-cases.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + '\n1..24\n'
+            + '# tests 24\n'
+            + '# pass  12\n'
+            + '# fail  12\n'
         );
     }));
 
     test('zeroes', function (t) {
         t.equal(0, -0, '0 equal to -0');
         t.equal(-0, 0, '-0 equal to 0');
+        t.notEqual(0, -0, '0 notEqual to -0');
+        t.notEqual(-0, 0, '-0 notEqual to 0');
 
         t.strictEqual(0, -0, '0 strictEqual to -0');
         t.strictEqual(-0, 0, '-0 strictEqual to 0');
+        t.notStrictEqual(0, -0, '0 notStrictEqual to -0');
+        t.notStrictEqual(-0, 0, '-0 notStrictEqual to 0');
 
         t.deepLooseEqual(0, -0, '0 deepLooseEqual to -0');
         t.deepLooseEqual(-0, 0, '-0 deepLooseEqual to 0');
+        t.notDeepLooseEqual(0, -0, '0 notDeepLooseEqual to -0');
+        t.notDeepLooseEqual(-0, 0, '-0 notDeepLooseEqual to 0');
 
         t.deepEqual(0, -0, '0 deepEqual to -0');
         t.deepEqual(-0, 0, '-0 deepEqual to 0');
+        t.notDeepEqual(0, -0, '0 notDeepEqual to -0');
+        t.notDeepEqual(-0, 0, '-0 notDeepEqual to 0');
 
         t.end();
     });
 
     test('NaNs', function (t) {
         t.equal(NaN, NaN, 'NaN equal to NaN');
+        t.notEqual(NaN, NaN, 'NaN notEqual to NaN');
 
         t.strictEqual(NaN, NaN, 'NaN strictEqual to NaN');
+        t.notStrictEqual(NaN, NaN, 'NaN notStrictEqual to NaN');
 
         t.deepLooseEqual(NaN, NaN, 'NaN deepLooseEqual to NaN');
+        t.notDeepLooseEqual(NaN, NaN, 'NaN notDeepLooseEqual to NaN');
 
         t.deepEqual(NaN, NaN, 'NaN deepEqual to NaN');
+        t.notDeepEqual(NaN, NaN, 'NaN notDeepEqual to NaN');
 
         t.end();
     });
diff --git a/test/numerics.js b/test/numerics.js
index 19392c18..7c3f7554 100644
--- a/test/numerics.js
+++ b/test/numerics.js
@@ -17,7 +17,31 @@ tap.test('numerics', function (tt) {
             + '# numeric strings\n'
             + 'ok 1 number equal to string\n'
             + 'ok 2 string equal to number\n'
-            + 'not ok 3 number strictEqual to string\n'
+            + 'not ok 3 number notEqual to string\n'
+            + '  ---\n'
+            + '    operator: notEqual\n'
+            + '    expected: \'3\'\n'
+            + '    actual:   3\n'
+            + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: number notEqual to string\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 4 string notEqual to number\n'
+            + '  ---\n'
+            + '    operator: notEqual\n'
+            + '    expected: 3\n'
+            + '    actual:   \'3\'\n'
+            + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: string notEqual to number\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 5 number strictEqual to string\n'
             + '  ---\n'
             + '    operator: strictEqual\n'
             + '    expected: \'3\'\n'
@@ -29,7 +53,7 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 4 string strictEqual to number\n'
+            + 'not ok 6 string strictEqual to number\n'
             + '  ---\n'
             + '    operator: strictEqual\n'
             + '    expected: 3\n'
@@ -41,9 +65,35 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'ok 5 number deepLooseEqual to string\n'
-            + 'ok 6 string deepLooseEqual to number\n'
-            + 'not ok 7 number deepEqual to string\n'
+            + 'ok 7 number notStrictEqual to string\n'
+            + 'ok 8 string notStrictEqual to number\n'
+            + 'ok 9 number deepLooseEqual to string\n'
+            + 'ok 10 string deepLooseEqual to number\n'
+            + 'not ok 11 number notDeepLooseEqual to string\n'
+            + '  ---\n'
+            + '    operator: notDeepLooseEqual\n'
+            + '    expected: \'3\'\n'
+            + '    actual:   3\n'
+            + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: number notDeepLooseEqual to string\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 12 string notDeepLooseEqual to number\n'
+            + '  ---\n'
+            + '    operator: notDeepLooseEqual\n'
+            + '    expected: 3\n'
+            + '    actual:   \'3\'\n'
+            + '    at: Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '    stack: |-\n'
+            + '      Error: string notDeepLooseEqual to number\n'
+            + '          [... stack stripped ...]\n'
+            + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
+            + '          [... stack stripped ...]\n'
+            + '  ...\n'
+            + 'not ok 13 number deepEqual to string\n'
             + '  ---\n'
             + '    operator: deepEqual\n'
             + '    expected: \'3\'\n'
@@ -55,7 +105,7 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + 'not ok 8 string deepEqual to number\n'
+            + 'not ok 14 string deepEqual to number\n'
             + '  ---\n'
             + '    operator: deepEqual\n'
             + '    expected: 3\n'
@@ -67,25 +117,35 @@ tap.test('numerics', function (tt) {
             + '          at Test.<anonymous> ($TEST/numerics.js:$LINE:$COL)\n'
             + '          [... stack stripped ...]\n'
             + '  ...\n'
-            + '\n1..8\n'
-            + '# tests 8\n'
-            + '# pass  4\n'
-            + '# fail  4\n'
+            + 'ok 15 number notDeepEqual to string\n'
+            + 'ok 16 string notDeepEqual to number\n'
+            + '\n1..16\n'
+            + '# tests 16\n'
+            + '# pass  8\n'
+            + '# fail  8\n'
         );
     }));
 
     test('numeric strings', function (t) {
         t.equal(3, '3', 'number equal to string');
         t.equal('3', 3, 'string equal to number');
+        t.notEqual(3, '3', 'number notEqual to string');
+        t.notEqual('3', 3, 'string notEqual to number');
 
         t.strictEqual(3, '3', 'number strictEqual to string');
         t.strictEqual('3', 3, 'string strictEqual to number');
+        t.notStrictEqual(3, '3', 'number notStrictEqual to string');
+        t.notStrictEqual('3', 3, 'string notStrictEqual to number');
 
         t.deepLooseEqual(3, '3', 'number deepLooseEqual to string');
         t.deepLooseEqual('3', 3, 'string deepLooseEqual to number');
+        t.notDeepLooseEqual(3, '3', 'number notDeepLooseEqual to string');
+        t.notDeepLooseEqual('3', 3, 'string notDeepLooseEqual to number');
 
         t.deepEqual(3, '3', 'number deepEqual to string');
         t.deepEqual('3', 3, 'string deepEqual to number');
+        t.notDeepEqual(3, '3', 'number notDeepEqual to string');
+        t.notDeepEqual('3', 3, 'string notDeepEqual to number');
 
         t.end();
     });