diff --git a/index.js b/index.js
index 188dab6..0d9cf53 100644
--- a/index.js
+++ b/index.js
@@ -34,6 +34,11 @@ var $setDelete = callBound('Set.prototype.delete', true);
 var $setHas = callBound('Set.prototype.has', true);
 var $setSize = callBound('Set.prototype.size', true);
 
+// the primitive that a boxed primitive wraps, read without calling a `valueOf` that the object may override
+function unbox(boxed, kind) {
+  return callBound(kind + '.prototype.valueOf')(boxed);
+}
+
 // taken from https://github.com/browserify/commonjs-assert/blob/bba838e9ba9e28edf3127ce6974624208502f6bc/internal/util/comparisons.js#L401-L414
 function setHasEqualElement(set, val1, opts, channel) {
   var i = getIterator(set);
@@ -130,6 +135,8 @@ function internalDeepEqual(actual, expected, options, channel) {
   if (actualBoxed !== expectedBoxed) {
     return false;
   }
+  // two boxed primitives of the same kind are equal only if the primitives they wrap are the same
+  if (actualBoxed && !is(unbox(actual, actualBoxed), unbox(expected, actualBoxed))) { return false; }
 
   // 7.3. Other pairs that do not both pass typeof value == 'object', equivalence is determined by ==.
   if (!actual || !expected || (typeof actual !== 'object' && typeof expected !== 'object')) {
diff --git a/test/cmp.js b/test/cmp.js
index fe24d1c..5d20755 100644
--- a/test/cmp.js
+++ b/test/cmp.js
@@ -1042,15 +1042,31 @@ test('boxed primitives', function (t) {
   t.deepEqualTest(Object(''), '', 'boxed and primitive `""`', false, false);
   t.deepEqualTest(Object('str'), 'str', 'boxed and primitive `"str"`', false, false);
 
+  t.deepEqualTest(Object(3), Object(3), 'two boxed `3`s', true, true);
+  t.deepEqualTest(Object(3), Object(4), 'boxed `3` and boxed `4`', false, false);
+  t.deepEqualTest(Object(NaN), Object(NaN), 'two boxed `NaN`s', true, true);
+  t.deepEqualTest(Object(0), Object(-0), 'boxed `0` and boxed `-0`', false, false);
+  t.deepEqualTest(Object(true), Object(true), 'two boxed `true`s', true, true);
+  t.deepEqualTest(Object(true), Object(false), 'boxed `true` and boxed `false`', false, false);
+  t.deepEqualTest(Object('str'), Object('str'), 'two boxed `"str"`s', true, true);
+  t.deepEqualTest(Object('str'), Object('other'), 'boxed `"str"` and boxed `"other"`', false, false);
+  t.deepEqualTest([Object(3)], [Object(4)], 'boxed numbers that differ, in arrays', false, false);
+  t.deepEqualTest({ a: Object(3) }, { a: Object(4) }, 'boxed numbers that differ, in objects', false, false);
+  t.deepEqualTest({ a: Object(3) }, { a: Object(3) }, 'boxed numbers that match, in objects', true, true);
+
   t.test('symbol', { skip: !hasSymbols }, function (st) {
     var s = Symbol('');
     st.deepEqualTest(Object(s), s, 'boxed and primitive `Symbol()`', false, false);
+    st.deepEqualTest(Object(s), Object(s), 'two boxes of the same `Symbol()`', true, true);
+    st.deepEqualTest(Object(s), Object(Symbol('')), 'boxes of two different symbols', false, false);
     st.end();
   });
 
   t.test('bigint', { skip: typeof BigInt !== 'function' }, function (st) {
     var hhgtg = BigInt(42);
     st.deepEqualTest(Object(hhgtg), hhgtg, 'boxed and primitive `BigInt(42)`', false, false);
+    st.deepEqualTest(Object(hhgtg), Object(BigInt(42)), 'two boxed `BigInt(42)`s', true, true);
+    st.deepEqualTest(Object(hhgtg), Object(BigInt(43)), 'boxed `BigInt(42)` and boxed `BigInt(43)`', false, false);
     st.end();
   });