diff --git a/lib/compress.js b/lib/compress.js
index b515c4259ce..4d9be943984 100644
--- a/lib/compress.js
+++ b/lib/compress.js
@@ -210,10 +210,19 @@ Compressor.prototype = new TreeTransformer(function(node, descend) {
     // output and performance.
     descend(node, this);
     var opt = node.optimize(this);
-    if (is_scope && opt === node && !this.has_directive("use asm") && !opt.pinned()) {
-        opt.drop_unused(this);
-        if (opt.merge_variables(this)) opt.drop_unused(this);
-        descend(opt, this);
+    if (is_scope) {
+        if (opt === node && !this.has_directive("use asm") && !opt.pinned()) {
+            opt.drop_unused(this);
+            if (opt.merge_variables(this)) opt.drop_unused(this);
+            descend(opt, this);
+        }
+        if (this.option("arrows") && is_arrow(opt) && opt.body.length == 1) {
+            var stat = opt.body[0];
+            if (stat instanceof AST_Return) {
+                opt.body.length = 0;
+                opt.value = stat.value;
+            }
+        }
     }
     if (opt === node) opt._squeezed = true;
     return opt;
@@ -6462,28 +6471,25 @@ Compressor.prototype.compress = function(node) {
         return self;
     });
 
-    function opt_arrow(self, compressor) {
-        if (!compressor.option("arrows")) return self;
-        drop_rest_farg(self, compressor);
-        if (self.value) self.body = [ self.first_statement() ];
-        var body = tighten_body(self.body, compressor);
-        switch (body.length) {
-          case 1:
-            var stat = body[0];
-            if (stat instanceof AST_Return) {
-                self.body.length = 0;
-                self.value = stat.value;
-                break;
-            }
-          default:
-            self.body = body;
-            self.value = null;
-            break;
+    function try_arrow(type, self, parent, compressor) {
+        if (!compressor.option("arrows")) return;
+        if (!compressor.option("module")) return;
+        if (self.name) return;
+        if (self.uses_arguments || self.pinned()) return;
+        var parent = compressor.parent();
+        if (parent instanceof AST_ClassMethod || parent instanceof AST_ObjectMethod) {
+            if (parent.value === self) return;
         }
-        return self;
+        if (self.contains_this()) return;
+        return make_node(type, self, self).optimize(compressor);
     }
-    OPT(AST_Arrow, opt_arrow);
-    OPT(AST_AsyncArrow, opt_arrow);
+
+    OPT(AST_AsyncFunction, function(self, compressor) {
+        drop_rest_farg(self, compressor);
+        self.body = tighten_body(self.body, compressor);
+        var arrow = try_arrow(AST_AsyncArrow, self, compressor.parent(), compressor);
+        return arrow ? arrow : self;
+    });
 
     OPT(AST_Function, function(self, compressor) {
         drop_rest_farg(self, compressor);
@@ -6547,7 +6553,8 @@ Compressor.prototype.compress = function(node) {
             }
             break;
         }
-        return self;
+        var arrow = try_arrow(AST_Arrow, self, parent, compressor);
+        return arrow ? arrow : self;
     });
 
     var NO_MERGE = makePredicate("arguments await yield");
diff --git a/test/compress/arrows.js b/test/compress/arrows.js
index b20316f8807..91aaba85e99 100644
--- a/test/compress/arrows.js
+++ b/test/compress/arrows.js
@@ -749,6 +749,42 @@ instanceof_lambda_4: {
     node_version: ">=4"
 }
 
+func_to_arrow: {
+    options = {
+        arrows: true,
+        module: true,
+    }
+    input: {
+        var f = function(a, b, c) {
+            return b + a + c + c;
+        };
+        console.log(f(...[].sort.call("SPA".split(""))));
+    }
+    expect: {
+        var f = (a, b, c) => b + a + c + c;
+        console.log(f(...[].sort.call("SPA".split(""))));
+    }
+    expect_stdout: "PASS"
+    node_version: ">=4"
+}
+
+iife_to_arrow: {
+    options = {
+        arrows: true,
+        module: true,
+    }
+    input: {
+        console.log(function(a, b, c) {
+            return b + a + c + c;
+        }(...[].sort.call("SPA".split(""))));
+    }
+    expect: {
+        console.log(((a, b, c) => b + a + c + c)(...[].sort.call("SPA".split(""))));
+    }
+    expect_stdout: "PASS"
+    node_version: ">=4"
+}
+
 issue_4388: {
     options = {
         inline: true,
@@ -1175,13 +1211,11 @@ issue_5416_1: {
     }
     expect: {
         var f = () => {
-            {
-                console;
-                arguments = void 0,
-                console.log(arguments);
-                var arguments;
-                return;
-            }
+            console;
+            arguments = void 0,
+            console.log(arguments);
+            var arguments;
+            return;
         };
         f();
     }
@@ -1210,12 +1244,10 @@ issue_5416_2: {
     }
     expect: {
         var f = () => {
-            {
-                console;
-                var arguments = void 0;
-                for (; console.log(arguments););
-                return;
-            }
+            console;
+            var arguments = void 0;
+            for (; console.log(arguments););
+            return;
         };
         f();
     }
@@ -1311,9 +1343,7 @@ issue_5653: {
         })());
     }
     expect: {
-        console.log((a => {
-            return +{};
-        })());
+        console.log((a => +{})());
     }
     expect_stdout: "NaN"
     node_version: ">=4"
diff --git a/test/compress/awaits.js b/test/compress/awaits.js
index 45d5dd3eca1..6e837ad33a6 100644
--- a/test/compress/awaits.js
+++ b/test/compress/awaits.js
@@ -1407,6 +1407,29 @@ instanceof_lambda_4: {
     node_version: ">=8"
 }
 
+async_to_arrow: {
+    options = {
+        arrows: true,
+        module: true,
+    }
+    input: {
+        (async function() {
+            var f = async function(a, b, c) {
+                return b + a + c + c;
+            };
+            console.log(await f(...[].sort.call("SPA".split(""))));
+        })();
+    }
+    expect: {
+        (async () => {
+            var f = async (a, b, c) => b + a + c + c;
+            console.log(await f(...[].sort.call("SPA".split(""))));
+        })();
+    }
+    expect_stdout: "PASS"
+    node_version: ">=8"
+}
+
 issue_4335_1: {
     options = {
         inline: true,
diff --git a/test/mocha/cli.js b/test/mocha/cli.js
index 2e7f8fe517f..010d28c9948 100644
--- a/test/mocha/cli.js
+++ b/test/mocha/cli.js
@@ -16,8 +16,9 @@ describe("bin/uglifyjs", function() {
         var command = [
             uglifyjscmd,
             "--self",
-            semver.satisfies(process.version, "<=0.12") ? "-mc hoist_funs" : "-mc",
             "--wrap WrappedUglifyJS",
+            semver.satisfies(process.version, "<4") ? "--no-module" : "--module",
+            semver.satisfies(process.version, "<=0.12") ? "-mc hoist_funs" : "-mc",
         ].join(" ");
         exec(command, { maxBuffer: 1048576 }, function(err, stdout) {
             if (err) throw err;
@@ -61,7 +62,7 @@ describe("bin/uglifyjs", function() {
             "--mangle",
         ].join(" "), function(err, stdout) {
             if (err) throw err;
-            assert.strictEqual(stdout, "function(n){for(;n(););return 42}(A)\n");
+            assert.strictEqual(stdout, "(r=>{for(;r(););return 42})(A)\n");
             done();
         }).stdin.end([
             "function(x) {",
@@ -1068,7 +1069,7 @@ describe("bin/uglifyjs", function() {
         ]).join("\n");
         exec(uglifyjscmd + " -mc", function(err, stdout) {
             if (err) throw err;
-            assert.strictEqual(stdout, "console.log(function(){var p={p:25},n={p:121},o={p:1024};return p.p+n.p+o.p}());\n");
+            assert.strictEqual(stdout, "console.log((()=>{var p={p:25},o={p:121},r={p:1024};return p.p+o.p+r.p})());\n");
             assert.strictEqual(run_code(stdout), run_code(code));
             done();
         }).stdin.end(code);
diff --git a/test/mocha/minify.js b/test/mocha/minify.js
index e63acd82d26..a9ef993980e 100644
--- a/test/mocha/minify.js
+++ b/test/mocha/minify.js
@@ -239,7 +239,7 @@ describe("minify", function() {
                 },
             });
             var code = result.code;
-            assert.strictEqual(code, "var a=function(){foo()}();");
+            assert.strictEqual(code, "var a=(()=>{foo()})();");
         });
     });
 
@@ -325,20 +325,30 @@ describe("minify", function() {
     });
 
     describe("module", function() {
-        it("Should not inline `await` variables", function() {
-            if (semver.satisfies(process.version, "<8")) return;
-            var code = [
-                "console.log(function() {",
-                "    return typeof await;",
-                "}());",
-            ].join("\n");
-            assert.strictEqual(run_code("(async function(){" + code + "})();"), "undefined\n");
+        var code = [
+            "console.log(function() {",
+            "    return typeof await;",
+            "}());",
+        ].join("\n");
+        it("Should inline `await` variables", function() {
+            var result = UglifyJS.minify(code, {
+                module: false,
+            });
+            if (result.error) throw result.error;
+            assert.strictEqual(result.code, "console.log(typeof await);");
+            assert.strictEqual(run_code(code), "undefined\n");
+            assert.strictEqual(run_code(result.code), "undefined\n");
+        });
+        it("Should not inline `await` variables in ES modules", function() {
             var result = UglifyJS.minify(code, {
                 module: true,
             });
             if (result.error) throw result.error;
-            assert.strictEqual(result.code, "console.log(function(){return typeof await}());");
-            assert.strictEqual(run_code("(async function(){" + result.code + "})();"), "undefined\n");
+            assert.strictEqual(result.code, "console.log((()=>typeof await)());");
+            if (semver.satisfies(process.version, ">=8")) {
+                assert.strictEqual(run_code("(async function(){" + code + "})();"), "undefined\n");
+                assert.strictEqual(run_code("(async function(){" + result.code + "})();"), "undefined\n");
+            }
         });
     });
 
diff --git a/test/mocha/sourcemaps.js b/test/mocha/sourcemaps.js
index 4efd42d13ce..4a74fdeda1c 100644
--- a/test/mocha/sourcemaps.js
+++ b/test/mocha/sourcemaps.js
@@ -301,14 +301,14 @@ describe("sourcemaps", function() {
             });
             if (result.error) throw result.error;
             var code = result.code;
-            assert.strictEqual(code, "var a=function(n){return n};\n" +
-                "//# sourceMappingURL=data:application/json;charset=utf-8;base64,eyJ2ZXJzaW9uIjozLCJzb3VyY2VzIjpbIjAiXSwibmFtZXMiOlsiYSIsImZvbyJdLCJtYXBwaW5ncyI6IkFBQUEsSUFBSUEsRUFBSSxTQUFTQyxHQUFPLE9BQU9BLENBQUsifQ==");
+            assert.strictEqual(code, "var a=a=>a;\n" +
+                "//# sourceMappingURL=data:application/json;charset=utf-8;base64,eyJ2ZXJzaW9uIjozLCJzb3VyY2VzIjpbIjAiXSwibmFtZXMiOlsiYSIsImZvbyJdLCJtYXBwaW5ncyI6IkFBQUEsSUFBSUEsRUFBYUMsR0FBY0EifQ==");
         });
         it("Should not append source map to output js when sourceMapInline is not enabled", function() {
             var result = UglifyJS.minify("var a = function(foo) { return foo; };");
             if (result.error) throw result.error;
             var code = result.code;
-            assert.strictEqual(code, "var a=function(n){return n};");
+            assert.strictEqual(code, "var a=a=>a;");
         });
         it("Should work with max_line_len", function() {
             var result = UglifyJS.minify(read("test/input/issue-505/input.js"), {
diff --git a/test/mocha/spidermonkey.js b/test/mocha/spidermonkey.js
index 79b0f29fd76..9babfc710f7 100644
--- a/test/mocha/spidermonkey.js
+++ b/test/mocha/spidermonkey.js
@@ -7,20 +7,21 @@ describe("spidermonkey export/import sanity test", function() {
     it("Should produce a functional build when using --self with spidermonkey", function(done) {
         this.timeout(120000);
         var uglifyjs = '"' + process.argv[0] + '" bin/uglifyjs';
-        var options = semver.satisfies(process.version, "<=0.12") ? "-mc hoist_funs" : "-mc";
+        var options = [
+            semver.satisfies(process.version, "<4") ? "--no-module" : "--module",
+            semver.satisfies(process.version, "<=0.12") ? "-mc hoist_funs" : "-mc",
+        ];
         var command = [
             [
                 uglifyjs,
                 "--self",
-                options,
                 "--wrap SpiderUglify",
                 "-o spidermonkey",
-            ].join(" "),
+            ].concat(options).join(" "),
             [
                 uglifyjs,
                 "-p spidermonkey",
-                options,
-            ].join(" "),
+            ].concat(options).join(" "),
         ].join(" | ");
         exec(command, { maxBuffer: 1048576 }, function(err, stdout) {
             if (err) throw err;