diff --git a/packages/babel-helper-replace-supers/src/index.js b/packages/babel-helper-replace-supers/src/index.js
index dff7328e68..139df00e4b 100644
--- a/packages/babel-helper-replace-supers/src/index.js
+++ b/packages/babel-helper-replace-supers/src/index.js
@@ -52,6 +52,10 @@ const visitor = {
     if (!path.isArrowFunctionExpression()) path.skip();
   },
 
+  ClassProperty(path) {
+    if (!path.node.static) path.skip();
+  },
+
   ReturnStatement(path, state) {
     if (!path.getFunctionParent().isArrowFunctionExpression()) {
       state.returns.push(path);
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-static-this-without-transform/actual.js b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-static-this-without-transform/actual.js
new file mode 100644
index 0000000000..2658970d52
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-static-this-without-transform/actual.js
@@ -0,0 +1,3 @@
+class Foo {
+  static fn = () => console.log(this);
+}
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-static-this-without-transform/expected.js b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-static-this-without-transform/expected.js
new file mode 100644
index 0000000000..7dc20a774c
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-static-this-without-transform/expected.js
@@ -0,0 +1,7 @@
+var _this = this;
+
+class Foo {
+  static fn = function () {
+    return console.log(_this);
+  };
+}
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-static-this-without-transform/options.json b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-static-this-without-transform/options.json
new file mode 100644
index 0000000000..5a9ea4593f
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-static-this-without-transform/options.json
@@ -0,0 +1,3 @@
+{
+  "plugins": ["external-helpers", "transform-es2015-arrow-functions", "syntax-class-properties"]
+}
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-this-without-transform/actual.js b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-this-without-transform/actual.js
new file mode 100644
index 0000000000..963f1aa2a6
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-this-without-transform/actual.js
@@ -0,0 +1,3 @@
+class Foo {
+  fn = () => console.log(this);
+}
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-this-without-transform/options.json b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-this-without-transform/options.json
new file mode 100644
index 0000000000..4f5f271f1a
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/general/arrow-this-without-transform/options.json
@@ -0,0 +1,4 @@
+{
+  "plugins": ["external-helpers", "transform-es2015-arrow-functions", "syntax-class-properties"],
+  "throws": "Unable to transform arrow inside class property"
+}
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6153/actual.js b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6153/actual.js
new file mode 100644
index 0000000000..d1a3e41179
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6153/actual.js
@@ -0,0 +1,28 @@
+() => {
+  class Foo {
+    fn = () => console.log(this);
+    static fn = () => console.log(this);
+  }
+};
+
+() => class Bar {
+  fn = () => console.log(this);
+  static fn = () => console.log(this);
+};
+
+() => {
+  class Baz {
+    fn = () => console.log(this);
+    force = force
+    static fn = () => console.log(this);
+
+    constructor(force) {}
+  }
+};
+
+var qux = function() {
+  class Qux {
+    fn = () => console.log(this);
+    static fn = () => console.log(this);
+  }
+}.bind(this)
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6153/expected.js b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6153/expected.js
new file mode 100644
index 0000000000..12a888802d
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6153/expected.js
@@ -0,0 +1,121 @@
+var _this = this;
+
+(function () {
+  class Foo {
+    constructor() {
+      var _this2 = this;
+
+      Object.defineProperty(this, "fn", {
+        configurable: true,
+        enumerable: true,
+        writable: true,
+        value: function () {
+          return console.log(_this2);
+        }
+      });
+    }
+
+  }
+
+  Object.defineProperty(Foo, "fn", {
+    configurable: true,
+    enumerable: true,
+    writable: true,
+    value: function () {
+      return console.log(_this);
+    }
+  });
+});
+
+(function () {
+  var _class, _temp;
+
+  return _temp = _class = class Bar {
+    constructor() {
+      var _this3 = this;
+
+      Object.defineProperty(this, "fn", {
+        configurable: true,
+        enumerable: true,
+        writable: true,
+        value: function () {
+          return console.log(_this3);
+        }
+      });
+    }
+
+  }, Object.defineProperty(_class, "fn", {
+    configurable: true,
+    enumerable: true,
+    writable: true,
+    value: function () {
+      return console.log(_this);
+    }
+  }), _temp;
+});
+
+(function () {
+  class Baz {
+    constructor(force) {
+      _initialiseProps.call(this);
+    }
+
+  }
+
+  Object.defineProperty(Baz, "fn", {
+    configurable: true,
+    enumerable: true,
+    writable: true,
+    value: function () {
+      return console.log(_this);
+    }
+  });
+
+  var _initialiseProps = function () {
+    var _this4 = this;
+
+    Object.defineProperty(this, "fn", {
+      configurable: true,
+      enumerable: true,
+      writable: true,
+      value: function () {
+        return console.log(_this4);
+      }
+    });
+    Object.defineProperty(this, "force", {
+      configurable: true,
+      enumerable: true,
+      writable: true,
+      value: force
+    });
+  };
+});
+
+var qux = function () {
+  var _this6 = this;
+
+  class Qux {
+    constructor() {
+      var _this5 = this;
+
+      Object.defineProperty(this, "fn", {
+        configurable: true,
+        enumerable: true,
+        writable: true,
+        value: function () {
+          return console.log(_this5);
+        }
+      });
+    }
+
+  }
+
+  Object.defineProperty(Qux, "fn", {
+    configurable: true,
+    enumerable: true,
+    writable: true,
+    value: function () {
+      return console.log(_this6);
+    }
+  });
+}.bind(this);
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6153/options.json b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6153/options.json
new file mode 100644
index 0000000000..4207909c7f
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6153/options.json
@@ -0,0 +1,3 @@
+{
+  "plugins": ["external-helpers", "transform-class-properties", "transform-es2015-arrow-functions"]
+}
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6154/actual.js b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6154/actual.js
new file mode 100644
index 0000000000..a08817f6a4
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6154/actual.js
@@ -0,0 +1,8 @@
+class Test {
+  constructor() {
+    class Other extends Test {
+      a = () => super.test;
+      static a = () => super.test;
+    }
+  }
+}
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6154/expected.js b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6154/expected.js
new file mode 100644
index 0000000000..5604d2ff3c
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6154/expected.js
@@ -0,0 +1,53 @@
+"use strict";
+
+var _typeof = typeof Symbol === "function" && typeof Symbol.iterator === "symbol" ? function (obj) { return typeof obj; } : function (obj) { return obj && typeof Symbol === "function" && obj.constructor === Symbol && obj !== Symbol.prototype ? "symbol" : typeof obj; };
+
+var _get = function get(object, property, receiver) { if (object === null) object = Function.prototype; var desc = Object.getOwnPropertyDescriptor(object, property); if (desc === undefined) { var parent = Object.getPrototypeOf(object); if (parent === null) { return undefined; } else { return get(parent, property, receiver); } } else if ("value" in desc) { return desc.value; } else { var getter = desc.get; if (getter === undefined) { return undefined; } return getter.call(receiver); } };
+
+function _possibleConstructorReturn(self, call) { if (call && (_typeof(call) === "object" || typeof call === "function")) { return call; } if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return self; }
+
+function _inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function"); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
+
+function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
+
+var Test = function Test() {
+  var _this2 = this;
+
+  _classCallCheck(this, Test);
+
+  var Other = function (_Test) {
+    _inherits(Other, _Test);
+
+    function Other() {
+      var _ref;
+
+      var _temp, _this;
+
+      _classCallCheck(this, Other);
+
+      for (var _len = arguments.length, args = Array(_len), _key = 0; _key < _len; _key++) {
+        args[_key] = arguments[_key];
+      }
+
+      return _possibleConstructorReturn(_this, (_temp = _this = _possibleConstructorReturn(this, (_ref = Other.__proto__ || Object.getPrototypeOf(Other)).call.apply(_ref, [this].concat(args))), Object.defineProperty(_this, "a", {
+        configurable: true,
+        enumerable: true,
+        writable: true,
+        value: function value() {
+          return _get(Other.prototype.__proto__ || Object.getPrototypeOf(Other.prototype), "test", _this);
+        }
+      }), _temp));
+    }
+
+    return Other;
+  }(Test);
+
+  Object.defineProperty(Other, "a", {
+    configurable: true,
+    enumerable: true,
+    writable: true,
+    value: function value() {
+      return _get(Test.prototype.__proto__ || Object.getPrototypeOf(Test.prototype), "test", _this2);
+    }
+  });
+};
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6154/options.json b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6154/options.json
new file mode 100644
index 0000000000..05581748b9
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/6154/options.json
@@ -0,0 +1,3 @@
+{
+  "presets": ["es2015", "stage-2"]
+}
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/regression/options.json b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/T2983/options.json
similarity index 100%
rename from packages/babel-plugin-transform-class-properties/test/fixtures/regression/options.json
rename to packages/babel-plugin-transform-class-properties/test/fixtures/regression/T2983/options.json
diff --git a/packages/babel-plugin-transform-class-properties/test/fixtures/regression/T6719/options.json b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/T6719/options.json
new file mode 100644
index 0000000000..79fb997f2d
--- /dev/null
+++ b/packages/babel-plugin-transform-class-properties/test/fixtures/regression/T6719/options.json
@@ -0,0 +1,3 @@
+{
+  "plugins": ["external-helpers", ["transform-class-properties",  {"loose": true}], "transform-es2015-classes", "transform-es2015-block-scoping", "syntax-class-properties"]
+}
diff --git a/packages/babel-traverse/src/path/conversion.js b/packages/babel-traverse/src/path/conversion.js
index 3ae7de7267..d145e3e840 100644
--- a/packages/babel-traverse/src/path/conversion.js
+++ b/packages/babel-traverse/src/path/conversion.js
@@ -123,7 +123,7 @@ function hoistFunctionEnvironment(
     p =>
       (p.isFunction() && !p.isArrowFunctionExpression()) ||
       p.isProgram() ||
-      p.isClassProperty(),
+      p.isClassProperty({ static: false }),
   );
   const inConstructor = thisEnvFn && thisEnvFn.node.kind === "constructor";
 
@@ -148,28 +148,22 @@ function hoistFunctionEnvironment(
         "Unable to handle nested super() usage in arrow",
       );
     }
-
     const allSuperCalls = [];
     thisEnvFn.traverse({
-      Function: child => {
-        if (
-          child.isArrowFunctionExpression() ||
-          child.isClassProperty() ||
-          child === fnPath
-        ) {
-          return;
-        }
+      Function(child) {
+        if (child.isArrowFunctionExpression()) return;
+        child.skip();
+      },
+      ClassProperty(child) {
+        if (child.node.static) return;
         child.skip();
       },
       CallExpression(child) {
         if (!child.get("callee").isSuper()) return;
-
         allSuperCalls.push(child);
       },
     });
-
     const superBinding = getSuperBinding(thisEnvFn);
-
     allSuperCalls.forEach(superCall =>
       superCall.get("callee").replaceWith(t.identifier(superBinding)),
     );
@@ -399,15 +393,12 @@ function getThisBinding(thisEnvFn, inConstructor) {
 
     const supers = new WeakSet();
     thisEnvFn.traverse({
-      Function: child => {
-        if (
-          child.isArrowFunctionExpression() ||
-          child.isClassProperty() ||
-          child === this
-        ) {
-          return;
-        }
-
+      Function(child) {
+        if (child.isArrowFunctionExpression()) return;
+        child.skip();
+      },
+      ClassProperty(child) {
+        if (child.node.static) return;
         child.skip();
       },
       CallExpression(child) {
@@ -529,8 +520,12 @@ function getScopeInformation(fnPath) {
   const superCalls = [];
 
   fnPath.traverse({
+    ClassProperty(child) {
+      if (child.node.static) return;
+      child.skip();
+    },
     Function(child) {
-      if (child.isArrowFunctionExpression() || child.isClassProperty()) return;
+      if (child.isArrowFunctionExpression()) return;
       child.skip();
     },
     ThisExpression(child) {