diff --git a/lib/compress/index.js b/lib/compress/index.js
index a5ca5b229..180487b01 100644
--- a/lib/compress/index.js
+++ b/lib/compress/index.js
@@ -5214,6 +5214,17 @@ def_optimize(AST_Call, function(self, compressor) {
             var args = self.args.concat(value);
             return make_sequence(self, args).optimize(compressor);
         }
+
+        // optimize identity function
+        if (
+            fn.argnames.length === 1
+            && self.args.length < 2
+            && value.start.type === "name"
+            && value.name === fn.argnames[0].name
+        ) {
+            // replace call with first argument or undefined if none passed
+            return (self.args[0] || make_node(AST_Undefined)).optimize(compressor);
+        }
     }
     if (can_inline) {
         var scope, in_loop, level = -1;
diff --git a/test/compress/async.js b/test/compress/async.js
index 69b00de36..5c97de30c 100644
--- a/test/compress/async.js
+++ b/test/compress/async.js
@@ -151,9 +151,9 @@ async_inline: {
         (async function(){ return await 3; })();
         (async function(x){ await console.log(x); })(4);
 
-        function echo(x) { return x; }
-        echo( async function(){ return await 1; }() );
-        echo( async function(x){ await console.log(x); }(2) );
+        function invoke(x, y) { return x(y); }
+        invoke( async function(){ return await 1; } );
+        invoke( async function(x){ await console.log(x); }, 2);
 
         function top() { console.log("top"); }
         top();
@@ -165,9 +165,9 @@ async_inline: {
         !async function(){await 3}();
         !async function(x){await console.log(4)}();
 
-        function echo(x){return x}
-        echo(async function(){return await 1}());
-        echo(async function(x){await console.log(2)}());
+        function invoke(x, y){return x(y)}
+        invoke(async function(){return await 1});
+        invoke(async function(x){await console.log(x)}, 2);
 
         console.log("top");
 
diff --git a/test/compress/functions.js b/test/compress/functions.js
index 47840fd22..86f86dd42 100644
--- a/test/compress/functions.js
+++ b/test/compress/functions.js
@@ -400,22 +400,22 @@ inner_ref: {
     input: {
         console.log(function(a) {
             return function() {
-                return a;
+                return a + 1;
             }();
         }(1), function(a) {
             return function(a) {
-                return a;
+                return a === undefined;
             }();
         }(2));
     }
     expect: {
-        console.log(function(a) {
-            return a;
-        }(1), function(a) {
-            return a;
+        console.log(function (a) {
+            return a + 1;
+        }(1), function (a) {
+            return void 0 === a;
         }());
     }
-    expect_stdout: "1 undefined"
+    expect_stdout: "2 true"
 }
 
 issue_2107: {
@@ -2102,15 +2102,15 @@ duplicate_arg_var: {
     }
     input: {
         console.log(function(b) {
-            return b;
+            return b + "ING";
             var b;
         }("PASS"));
     }
     expect: {
-        console.log((b = "PASS", b));
+        console.log((b = "PASS", b + "ING"));
         var b;
     }
-    expect_stdout: "PASS"
+    expect_stdout: "PASSING"
 }
 
 issue_2737_1: {
diff --git a/test/compress/identity.js b/test/compress/identity.js
new file mode 100644
index 000000000..3234b44f2
--- /dev/null
+++ b/test/compress/identity.js
@@ -0,0 +1,164 @@
+inline_identity: {
+    options = {
+        inline: true,
+        reduce_vars: true,
+        unused: true,
+        toplevel: true
+    }
+    input: {
+        const id = x => x;
+        console.log(id(1), id(2));
+    }
+    expect: {
+        console.log(1, 2);
+    }
+    expect_stdout: "1 2"
+}
+
+inline_identity_function: {
+    options = {
+        inline: true,
+        reduce_vars: true,
+        unused: true,
+        toplevel: true
+    }
+    input: {
+        function id(x) { return x };
+        console.log(id(1), id(2));
+    }
+    expect: {
+        console.log(1, 2);
+    }
+    expect_stdout: "1 2"
+}
+
+inline_identity_undefined: {
+    options = {
+        inline: true,
+        reduce_vars: true,
+        unused: true,
+        toplevel: true
+    }
+    input: {
+        const id = x => x;
+        console.log(id(), id(undefined));
+    }
+    expect: {
+        console.log(void 0, void 0);
+    }
+    expect_stdout: "undefined undefined"
+}
+
+inline_identity_extra_params: {
+    options = {
+        inline: true,
+        reduce_vars: true,
+        unused: true,
+        toplevel: true
+    }
+    input: {
+        const id = x => x;
+        console.log(id(1, console.log(2)), id(3, 4));
+    }
+    expect: {
+        const id = x => x;
+        console.log(id(1, console.log(2)), 3);
+    }
+    expect_stdout: ["2", "1 3"]
+}
+
+inline_identity_higher_order: {
+    options = {
+        inline: true,
+        reduce_vars: true,
+        unused: true,
+        toplevel: true
+    }
+    input: {
+        const id = x => x;
+        const inc = x => x + 1;
+        console.log(id(inc(1)), id(inc)(2));
+    }
+    expect: {
+        const inc = x => x + 1;
+        console.log(inc(1), inc(2));
+    }
+    expect_stdout: "2 3"
+}
+
+inline_identity_inline_function: {
+    options = {
+        evaluate: true,
+        inline: true,
+        passes: 2,
+        reduce_vars: true,
+        unused: true,
+        toplevel: true
+    }
+    input: {
+        const id = x => x;
+        console.log(id(x => x + 1)(1), id((x => x + 1)(2)));
+    }
+    expect: {
+        console.log(2, 3);
+    }
+    expect_stdout: "2 3"
+}
+
+inline_identity_duplicate_arg_var: {
+    options = {
+        inline: true,
+        reduce_vars: true,
+        unused: true,
+        toplevel: true
+    }
+    input: {
+        const id = x => {
+            return x;
+            var x;
+        };
+        console.log(id(1), id(2));
+    }
+    expect: {
+        console.log(1, 2);
+    }
+    expect_stdout: "1 2"
+}
+
+inline_identity_inner_ref: {
+    options = {
+        inline: true,
+        reduce_vars: true,
+        unused: true,
+        toplevel: true
+    }
+    input: {
+        const id = a => (function() { return a; })();
+        const undef = a => (a => a)();
+        console.log(id(1), id(2), undef(3), undef(4));
+    }
+    expect: {
+        console.log(1, 2, void 0, void 0);
+    }
+    expect_stdout: "1 2 undefined undefined"
+}
+
+inline_identity_async: {
+    options = {
+        inline: true,
+        reduce_vars: true,
+        unused: true,
+        toplevel: true
+    }
+    input: {
+        const id = x => x;
+        id(async () => await 1)();
+        id(async x => await console.log(2))();
+    }
+    expect: {
+        (async () => await 1)();
+        (async x => await console.log(2))();
+    }
+    expect_stdout: "2"
+    node_version: ">=8"
+}
diff --git a/test/compress/reduce_vars.js b/test/compress/reduce_vars.js
index e6a9203e2..c9e94843a 100644
--- a/test/compress/reduce_vars.js
+++ b/test/compress/reduce_vars.js
@@ -1429,6 +1429,7 @@ defun_inline_3: {
 
 defun_call: {
     options = {
+        evaluate: true,
         inline: true,
         reduce_funcs: true,
         reduce_vars: true,
@@ -1447,10 +1448,7 @@ defun_call: {
     }
     expect: {
         function f() {
-            return 4 + h(1) - h(4);
-            function h(a) {
-                return a;
-            }
+            return 1;
         }
     }
 }