diff --git a/example/example4.cpp b/example/example4.cpp
index 9865931..e673c4a 100644
--- a/example/example4.cpp
+++ b/example/example4.cpp
@@ -21,8 +21,9 @@
         ESecondMode
     };
 
-    static void test_function(EMode mode) {
+    static EMode test_function(EMode mode) {
         std::cout << "Example4::test_function(enum=" << mode << ")" << std::endl;
+        return mode;
     }
 };
 
@@ -42,7 +43,7 @@
 
 py::bytes return_bytes() {
     const char *data = "\x01\x00\x02\x00";
-    return py::bytes(std::string(data, 4));
+    return std::string(data, 4);
 }
 
 void print_bytes(py::bytes bytes) {
diff --git a/example/example4.py b/example/example4.py
index 74f860d..37d952f 100755
--- a/example/example4.py
+++ b/example/example4.py
@@ -20,10 +20,39 @@
 print(test_function(7))
 print(test_function(EMyEnumeration.EFirstEntry))
 print(test_function(EMyEnumeration.ESecondEntry))
+print("enum->integer = %i" % int(EMyEnumeration.ESecondEntry))
+print("integer->enum = %s" % str(EMyEnumeration(2)))
+
+print("A constant = " + str(some_constant))
 
 print(Example4.EMode)
 print(Example4.EMode.EFirstMode)
 print(Example4.EFirstMode)
 Example4.test_function(Example4.EFirstMode)
 
+print("Equality test 1: " + str(
+    Example4.test_function(Example4.EFirstMode) ==
+    Example4.test_function(Example4.EFirstMode)))
+
+print("Inequality test 1: " + str(
+    Example4.test_function(Example4.EFirstMode) !=
+    Example4.test_function(Example4.EFirstMode)))
+
+print("Equality test 2: " + str(
+    Example4.test_function(Example4.EFirstMode) ==
+    Example4.test_function(Example4.ESecondMode)))
+
+print("Inequality test 2: " + str(
+    Example4.test_function(Example4.EFirstMode) !=
+    Example4.test_function(Example4.ESecondMode)))
+
+x = {
+        Example4.test_function(Example4.EFirstMode): 1,
+        Example4.test_function(Example4.ESecondMode): 2
+}
+
+x[Example4.test_function(Example4.EFirstMode)] = 3
+x[Example4.test_function(Example4.ESecondMode)] = 4
+print("Hashing test = " + str(x))
+
 print_bytes(return_bytes())
diff --git a/example/example4.ref b/example/example4.ref
index 040d55b..a21f62c 100644
--- a/example/example4.ref
+++ b/example/example4.ref
@@ -10,10 +10,30 @@
 None
 test_function(enum=2)
 None
+enum->integer = 2
+integer->enum = EMyEnumeration.ESecondEntry
+A constant = 14
 <class 'example.EMode'>
 EMode.EFirstMode
 EMode.EFirstMode
 Example4::test_function(enum=1)
+Example4::test_function(enum=1)
+Example4::test_function(enum=1)
+Equality test 1: True
+Example4::test_function(enum=1)
+Example4::test_function(enum=1)
+Inequality test 1: False
+Example4::test_function(enum=1)
+Example4::test_function(enum=2)
+Equality test 2: False
+Example4::test_function(enum=1)
+Example4::test_function(enum=2)
+Inequality test 2: True
+Example4::test_function(enum=1)
+Example4::test_function(enum=2)
+Example4::test_function(enum=1)
+Example4::test_function(enum=2)
+Hashing test = {EMode.EFirstMode: 3, EMode.ESecondMode: 4}
 bytes[0]=1
 bytes[1]=0
 bytes[2]=2
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index bbcda47..166966a 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -907,7 +907,11 @@
                 ((it == entries->end()) ? std::string("???")
                                         : std::string(it->second));
         });
+        this->def("__init__", [](Type& value, int i) { value = (Type) i; });
         this->def("__int__", [](Type value) { return (int) value; });
+        this->def("__eq__", [](const Type &value, Type value2) { return value == value2; });
+        this->def("__ne__", [](const Type &value, Type value2) { return value != value2; });
+        this->def("__hash__", [](const Type &value) { return (int) value; });
         m_entries = entries;
     }