diff --git a/src/compiler/checker.ts b/src/compiler/checker.ts
index 4ee4b17e4e5..c3dff2371e7 100644
--- a/src/compiler/checker.ts
+++ b/src/compiler/checker.ts
@@ -8520,15 +8520,14 @@ namespace ts {
         function getContextuallyTypedParameterType(parameter: ParameterDeclaration): Type {
             const func = parameter.parent;
             if (isContextSensitiveFunctionOrObjectLiteralMethod(func)) {
-                if (isIife(func)) {
+                const iife = getImmediatelyInvokedFunctionExpression(func);
+                if (iife) {
                     const indexOfParameter = indexOf(func.parameters, parameter);
-                    const call = func.parent.parent as CallExpression;
-                    if (indexOfParameter < call.arguments.length) {
-                        const type = getTypeOfExpression(call.arguments[indexOfParameter]);
-                        if (type && parameter.dotDotDotToken) {
-                            return createArrayType(type);
+                    if (iife.arguments && indexOfParameter < iife.arguments.length) {
+                        if (parameter.dotDotDotToken) {
+                            return createArrayType(getUnionType(map(iife.arguments.slice(indexOfParameter), getTypeOfExpression)));
                         }
-                        return type;
+                        return checkExpression(iife.arguments[indexOfParameter], identityMapper);
                     }
                 }
                 const contextualSignature = getContextualSignature(func);
@@ -8551,11 +8550,16 @@ namespace ts {
             return undefined;
         }
 
-        function isIife(func: FunctionExpression | MethodDeclaration) {
-            return (func.kind === SyntaxKind.FunctionExpression || func.kind === SyntaxKind.ArrowFunction) &&
-                func.parent.kind === SyntaxKind.ParenthesizedExpression &&
-                func.parent.parent.kind === SyntaxKind.CallExpression &&
-                (func.parent.parent as CallExpression).expression === func.parent;
+        function getImmediatelyInvokedFunctionExpression(func: FunctionExpression | MethodDeclaration) {
+            if (isFunctionExpressionOrArrowFunction(func)) {
+                let parent = func.parent;
+                while (parent.kind === SyntaxKind.ParenthesizedExpression) {
+                    parent = parent.parent;
+                }
+                if (parent.kind === SyntaxKind.CallExpression) {
+                    return parent as CallExpression;
+                }
+            }
         }
 
         // In a variable, parameter or property declaration with a type annotation,
diff --git a/tests/baselines/reference/contextuallyTypedIife.js b/tests/baselines/reference/contextuallyTypedIife.js
index 544acea0a46..0a84e45e30b 100644
--- a/tests/baselines/reference/contextuallyTypedIife.js
+++ b/tests/baselines/reference/contextuallyTypedIife.js
@@ -3,10 +3,11 @@
 (jake => { })("build");
 // function expression
 (function (cats) { })("lol");
+// Lots of Irritating Superfluous Parentheses
+(function (x) { } ("!"));
+((((function (y) { }))))("-");
 // multiple arguments
 ((a, b, c) => { })("foo", 101, false);
-// contextually typed parameters.
-(f => f(1))(i => i + 1);
 // default parameters
 ((m = 10) => m + 1)(12);
 ((n = 10) => n + 1)();
@@ -16,6 +17,7 @@
 ((l, o?) => l + o)(12); // o should be any
 // rest parameters
 ((...numbers) => numbers.every(n => n > 0))(5,6,7);
+((...mixed) => mixed.every(n => !!n))(5,'oops','oh no');
 ((...noNumbers) => noNumbers.some(n => n > 0))();
 ((first, ...rest) => first ? [] : rest.map(n => n > 0))(8,9,10);
 // destructuring parameters (with defaults too!)
@@ -23,8 +25,9 @@
 (({ p = 14 }) => p)({ p : 15 });
 (({ r = 17 } = { r: 18 }) => r)({r : 19});
 (({ u = 22 } = { u: 23 }) => u)();
-
-
+// contextually typed parameters.
+let twelve = (f => f(12))(i => i);
+let eleven = (o => o.a(11))({ a: function(n) { return n; } });
 
 
 //// [contextuallyTypedIife.js]
@@ -32,10 +35,11 @@
 (function (jake) { })("build");
 // function expression
 (function (cats) { })("lol");
+// Lots of Irritating Superfluous Parentheses
+(function (x) { }("!"));
+((((function (y) { }))))("-");
 // multiple arguments
 (function (a, b, c) { })("foo", 101, false);
-// contextually typed parameters.
-(function (f) { return f(1); })(function (i) { return i + 1; });
 // default parameters
 (function (m) {
     if (m === void 0) { m = 10; }
@@ -57,6 +61,13 @@
     }
     return numbers.every(function (n) { return n > 0; });
 })(5, 6, 7);
+(function () {
+    var mixed = [];
+    for (var _i = 0; _i < arguments.length; _i++) {
+        mixed[_i - 0] = arguments[_i];
+    }
+    return mixed.every(function (n) { return !!n; });
+})(5, 'oops', 'oh no');
 (function () {
     var noNumbers = [];
     for (var _i = 0; _i < arguments.length; _i++) {
@@ -88,3 +99,6 @@
     var _b = (_a === void 0 ? { u: 23 } : _a).u, u = _b === void 0 ? 22 : _b;
     return u;
 })();
+// contextually typed parameters.
+var twelve = (function (f) { return f(12); })(function (i) { return i; });
+var eleven = (function (o) { return o.a(11); })({ a: function (n) { return n; } });
diff --git a/tests/baselines/reference/contextuallyTypedIife.symbols b/tests/baselines/reference/contextuallyTypedIife.symbols
index 01001dc0f32..824ce6031ce 100644
--- a/tests/baselines/reference/contextuallyTypedIife.symbols
+++ b/tests/baselines/reference/contextuallyTypedIife.symbols
@@ -7,91 +7,115 @@
 (function (cats) { })("lol");
 >cats : Symbol(cats, Decl(contextuallyTypedIife.ts, 3, 11))
 
+// Lots of Irritating Superfluous Parentheses
+(function (x) { } ("!"));
+>x : Symbol(x, Decl(contextuallyTypedIife.ts, 5, 11))
+
+((((function (y) { }))))("-");
+>y : Symbol(y, Decl(contextuallyTypedIife.ts, 6, 14))
+
 // multiple arguments
 ((a, b, c) => { })("foo", 101, false);
->a : Symbol(a, Decl(contextuallyTypedIife.ts, 5, 2))
->b : Symbol(b, Decl(contextuallyTypedIife.ts, 5, 4))
->c : Symbol(c, Decl(contextuallyTypedIife.ts, 5, 7))
-
-// contextually typed parameters.
-(f => f(1))(i => i + 1);
->f : Symbol(f, Decl(contextuallyTypedIife.ts, 7, 1))
->f : Symbol(f, Decl(contextuallyTypedIife.ts, 7, 1))
->i : Symbol(i, Decl(contextuallyTypedIife.ts, 7, 12))
->i : Symbol(i, Decl(contextuallyTypedIife.ts, 7, 12))
+>a : Symbol(a, Decl(contextuallyTypedIife.ts, 8, 2))
+>b : Symbol(b, Decl(contextuallyTypedIife.ts, 8, 4))
+>c : Symbol(c, Decl(contextuallyTypedIife.ts, 8, 7))
 
 // default parameters
 ((m = 10) => m + 1)(12);
->m : Symbol(m, Decl(contextuallyTypedIife.ts, 9, 2))
->m : Symbol(m, Decl(contextuallyTypedIife.ts, 9, 2))
+>m : Symbol(m, Decl(contextuallyTypedIife.ts, 10, 2))
+>m : Symbol(m, Decl(contextuallyTypedIife.ts, 10, 2))
 
 ((n = 10) => n + 1)();
->n : Symbol(n, Decl(contextuallyTypedIife.ts, 10, 2))
->n : Symbol(n, Decl(contextuallyTypedIife.ts, 10, 2))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 11, 2))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 11, 2))
 
 // optional parameters
 ((j?) => j + 1)(12);
->j : Symbol(j, Decl(contextuallyTypedIife.ts, 12, 2))
->j : Symbol(j, Decl(contextuallyTypedIife.ts, 12, 2))
+>j : Symbol(j, Decl(contextuallyTypedIife.ts, 13, 2))
+>j : Symbol(j, Decl(contextuallyTypedIife.ts, 13, 2))
 
 ((k?) => k + 1)();
->k : Symbol(k, Decl(contextuallyTypedIife.ts, 13, 2))
->k : Symbol(k, Decl(contextuallyTypedIife.ts, 13, 2))
+>k : Symbol(k, Decl(contextuallyTypedIife.ts, 14, 2))
+>k : Symbol(k, Decl(contextuallyTypedIife.ts, 14, 2))
 
 ((l, o?) => l + o)(12); // o should be any
->l : Symbol(l, Decl(contextuallyTypedIife.ts, 14, 2))
->o : Symbol(o, Decl(contextuallyTypedIife.ts, 14, 4))
->l : Symbol(l, Decl(contextuallyTypedIife.ts, 14, 2))
->o : Symbol(o, Decl(contextuallyTypedIife.ts, 14, 4))
+>l : Symbol(l, Decl(contextuallyTypedIife.ts, 15, 2))
+>o : Symbol(o, Decl(contextuallyTypedIife.ts, 15, 4))
+>l : Symbol(l, Decl(contextuallyTypedIife.ts, 15, 2))
+>o : Symbol(o, Decl(contextuallyTypedIife.ts, 15, 4))
 
 // rest parameters
 ((...numbers) => numbers.every(n => n > 0))(5,6,7);
->numbers : Symbol(numbers, Decl(contextuallyTypedIife.ts, 16, 2))
+>numbers : Symbol(numbers, Decl(contextuallyTypedIife.ts, 17, 2))
 >numbers.every : Symbol(Array.every, Decl(lib.d.ts, --, --))
->numbers : Symbol(numbers, Decl(contextuallyTypedIife.ts, 16, 2))
+>numbers : Symbol(numbers, Decl(contextuallyTypedIife.ts, 17, 2))
 >every : Symbol(Array.every, Decl(lib.d.ts, --, --))
->n : Symbol(n, Decl(contextuallyTypedIife.ts, 16, 31))
->n : Symbol(n, Decl(contextuallyTypedIife.ts, 16, 31))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 17, 31))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 17, 31))
+
+((...mixed) => mixed.every(n => !!n))(5,'oops','oh no');
+>mixed : Symbol(mixed, Decl(contextuallyTypedIife.ts, 18, 2))
+>mixed.every : Symbol(Array.every, Decl(lib.d.ts, --, --))
+>mixed : Symbol(mixed, Decl(contextuallyTypedIife.ts, 18, 2))
+>every : Symbol(Array.every, Decl(lib.d.ts, --, --))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 18, 27))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 18, 27))
 
 ((...noNumbers) => noNumbers.some(n => n > 0))();
->noNumbers : Symbol(noNumbers, Decl(contextuallyTypedIife.ts, 17, 2))
+>noNumbers : Symbol(noNumbers, Decl(contextuallyTypedIife.ts, 19, 2))
 >noNumbers.some : Symbol(Array.some, Decl(lib.d.ts, --, --))
->noNumbers : Symbol(noNumbers, Decl(contextuallyTypedIife.ts, 17, 2))
+>noNumbers : Symbol(noNumbers, Decl(contextuallyTypedIife.ts, 19, 2))
 >some : Symbol(Array.some, Decl(lib.d.ts, --, --))
->n : Symbol(n, Decl(contextuallyTypedIife.ts, 17, 34))
->n : Symbol(n, Decl(contextuallyTypedIife.ts, 17, 34))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 19, 34))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 19, 34))
 
 ((first, ...rest) => first ? [] : rest.map(n => n > 0))(8,9,10);
->first : Symbol(first, Decl(contextuallyTypedIife.ts, 18, 2))
->rest : Symbol(rest, Decl(contextuallyTypedIife.ts, 18, 8))
->first : Symbol(first, Decl(contextuallyTypedIife.ts, 18, 2))
+>first : Symbol(first, Decl(contextuallyTypedIife.ts, 20, 2))
+>rest : Symbol(rest, Decl(contextuallyTypedIife.ts, 20, 8))
+>first : Symbol(first, Decl(contextuallyTypedIife.ts, 20, 2))
 >rest.map : Symbol(Array.map, Decl(lib.d.ts, --, --))
->rest : Symbol(rest, Decl(contextuallyTypedIife.ts, 18, 8))
+>rest : Symbol(rest, Decl(contextuallyTypedIife.ts, 20, 8))
 >map : Symbol(Array.map, Decl(lib.d.ts, --, --))
->n : Symbol(n, Decl(contextuallyTypedIife.ts, 18, 43))
->n : Symbol(n, Decl(contextuallyTypedIife.ts, 18, 43))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 20, 43))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 20, 43))
 
 // destructuring parameters (with defaults too!)
 (({ q }) => q)({ q : 13 });
->q : Symbol(q, Decl(contextuallyTypedIife.ts, 20, 3))
->q : Symbol(q, Decl(contextuallyTypedIife.ts, 20, 3))
->q : Symbol(q, Decl(contextuallyTypedIife.ts, 20, 16))
+>q : Symbol(q, Decl(contextuallyTypedIife.ts, 22, 3))
+>q : Symbol(q, Decl(contextuallyTypedIife.ts, 22, 3))
+>q : Symbol(q, Decl(contextuallyTypedIife.ts, 22, 16))
 
 (({ p = 14 }) => p)({ p : 15 });
->p : Symbol(p, Decl(contextuallyTypedIife.ts, 21, 3))
->p : Symbol(p, Decl(contextuallyTypedIife.ts, 21, 3))
->p : Symbol(p, Decl(contextuallyTypedIife.ts, 21, 21))
+>p : Symbol(p, Decl(contextuallyTypedIife.ts, 23, 3))
+>p : Symbol(p, Decl(contextuallyTypedIife.ts, 23, 3))
+>p : Symbol(p, Decl(contextuallyTypedIife.ts, 23, 21))
 
 (({ r = 17 } = { r: 18 }) => r)({r : 19});
->r : Symbol(r, Decl(contextuallyTypedIife.ts, 22, 3))
->r : Symbol(r, Decl(contextuallyTypedIife.ts, 22, 16))
->r : Symbol(r, Decl(contextuallyTypedIife.ts, 22, 3))
->r : Symbol(r, Decl(contextuallyTypedIife.ts, 22, 33))
+>r : Symbol(r, Decl(contextuallyTypedIife.ts, 24, 3))
+>r : Symbol(r, Decl(contextuallyTypedIife.ts, 24, 16))
+>r : Symbol(r, Decl(contextuallyTypedIife.ts, 24, 3))
+>r : Symbol(r, Decl(contextuallyTypedIife.ts, 24, 33))
 
 (({ u = 22 } = { u: 23 }) => u)();
->u : Symbol(u, Decl(contextuallyTypedIife.ts, 23, 3))
->u : Symbol(u, Decl(contextuallyTypedIife.ts, 23, 16))
->u : Symbol(u, Decl(contextuallyTypedIife.ts, 23, 3))
+>u : Symbol(u, Decl(contextuallyTypedIife.ts, 25, 3))
+>u : Symbol(u, Decl(contextuallyTypedIife.ts, 25, 16))
+>u : Symbol(u, Decl(contextuallyTypedIife.ts, 25, 3))
 
+// contextually typed parameters.
+let twelve = (f => f(12))(i => i);
+>twelve : Symbol(twelve, Decl(contextuallyTypedIife.ts, 27, 3))
+>f : Symbol(f, Decl(contextuallyTypedIife.ts, 27, 14))
+>f : Symbol(f, Decl(contextuallyTypedIife.ts, 27, 14))
+>i : Symbol(i, Decl(contextuallyTypedIife.ts, 27, 26))
+>i : Symbol(i, Decl(contextuallyTypedIife.ts, 27, 26))
 
+let eleven = (o => o.a(11))({ a: function(n) { return n; } });
+>eleven : Symbol(eleven, Decl(contextuallyTypedIife.ts, 28, 3))
+>o : Symbol(o, Decl(contextuallyTypedIife.ts, 28, 14))
+>o.a : Symbol(a, Decl(contextuallyTypedIife.ts, 28, 29))
+>o : Symbol(o, Decl(contextuallyTypedIife.ts, 28, 14))
+>a : Symbol(a, Decl(contextuallyTypedIife.ts, 28, 29))
+>a : Symbol(a, Decl(contextuallyTypedIife.ts, 28, 29))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 28, 42))
+>n : Symbol(n, Decl(contextuallyTypedIife.ts, 28, 42))
 
diff --git a/tests/baselines/reference/contextuallyTypedIife.types b/tests/baselines/reference/contextuallyTypedIife.types
index b2fc85dddfd..b673927e174 100644
--- a/tests/baselines/reference/contextuallyTypedIife.types
+++ b/tests/baselines/reference/contextuallyTypedIife.types
@@ -15,6 +15,24 @@
 >cats : string
 >"lol" : string
 
+// Lots of Irritating Superfluous Parentheses
+(function (x) { } ("!"));
+>(function (x) { } ("!")) : void
+>function (x) { } ("!") : void
+>function (x) { } : (x: string) => void
+>x : string
+>"!" : string
+
+((((function (y) { }))))("-");
+>((((function (y) { }))))("-") : void
+>((((function (y) { })))) : (y: string) => void
+>(((function (y) { }))) : (y: string) => void
+>((function (y) { })) : (y: string) => void
+>(function (y) { }) : (y: string) => void
+>function (y) { } : (y: string) => void
+>y : string
+>"-" : string
+
 // multiple arguments
 ((a, b, c) => { })("foo", 101, false);
 >((a, b, c) => { })("foo", 101, false) : void
@@ -27,21 +45,6 @@
 >101 : number
 >false : boolean
 
-// contextually typed parameters.
-(f => f(1))(i => i + 1);
->(f => f(1))(i => i + 1) : any
->(f => f(1)) : (f: (i: any) => any) => any
->f => f(1) : (f: (i: any) => any) => any
->f : (i: any) => any
->f(1) : any
->f : (i: any) => any
->1 : number
->i => i + 1 : (i: any) => any
->i : any
->i + 1 : any
->i : any
->1 : number
-
 // default parameters
 ((m = 10) => m + 1)(12);
 >((m = 10) => m + 1)(12) : number
@@ -114,6 +117,24 @@
 >6 : number
 >7 : number
 
+((...mixed) => mixed.every(n => !!n))(5,'oops','oh no');
+>((...mixed) => mixed.every(n => !!n))(5,'oops','oh no') : boolean
+>((...mixed) => mixed.every(n => !!n)) : (...mixed: (number | string)[]) => boolean
+>(...mixed) => mixed.every(n => !!n) : (...mixed: (number | string)[]) => boolean
+>mixed : (number | string)[]
+>mixed.every(n => !!n) : boolean
+>mixed.every : (callbackfn: (value: number | string, index: number, array: (number | string)[]) => boolean, thisArg?: any) => boolean
+>mixed : (number | string)[]
+>every : (callbackfn: (value: number | string, index: number, array: (number | string)[]) => boolean, thisArg?: any) => boolean
+>n => !!n : (n: number | string) => boolean
+>n : number | string
+>!!n : boolean
+>!n : boolean
+>n : number | string
+>5 : number
+>'oops' : string
+>'oh no' : string
+
 ((...noNumbers) => noNumbers.some(n => n > 0))();
 >((...noNumbers) => noNumbers.some(n => n > 0))() : boolean
 >((...noNumbers) => noNumbers.some(n => n > 0)) : (...noNumbers: any[]) => boolean
@@ -198,5 +219,34 @@
 >23 : number
 >u : number
 
+// contextually typed parameters.
+let twelve = (f => f(12))(i => i);
+>twelve : any
+>(f => f(12))(i => i) : any
+>(f => f(12)) : (f: {}) => any
+>f => f(12) : (f: {}) => any
+>f : {}
+>f(12) : any
+>f : {}
+>12 : number
+>i => i : (i: {}) => {}
+>i : {}
+>i : {}
 
+let eleven = (o => o.a(11))({ a: function(n) { return n; } });
+>eleven : any
+>(o => o.a(11))({ a: function(n) { return n; } }) : any
+>(o => o.a(11)) : (o: { a: {}; }) => any
+>o => o.a(11) : (o: { a: {}; }) => any
+>o : { a: {}; }
+>o.a(11) : any
+>o.a : {}
+>o : { a: {}; }
+>a : {}
+>11 : number
+>{ a: function(n) { return n; } } : { a: (n: any) => any; }
+>a : (n: any) => any
+>function(n) { return n; } : (n: any) => any
+>n : any
+>n : any
 
diff --git a/tests/cases/conformance/expressions/functions/contextuallyTypedIife.ts b/tests/cases/conformance/expressions/functions/contextuallyTypedIife.ts
index 169f5ffecf0..ed3c24e0ac7 100644
--- a/tests/cases/conformance/expressions/functions/contextuallyTypedIife.ts
+++ b/tests/cases/conformance/expressions/functions/contextuallyTypedIife.ts
@@ -2,10 +2,11 @@
 (jake => { })("build");
 // function expression
 (function (cats) { })("lol");
+// Lots of Irritating Superfluous Parentheses
+(function (x) { } ("!"));
+((((function (y) { }))))("-");
 // multiple arguments
 ((a, b, c) => { })("foo", 101, false);
-// contextually typed parameters.
-(f => f(1))(i => i + 1);
 // default parameters
 ((m = 10) => m + 1)(12);
 ((n = 10) => n + 1)();
@@ -15,6 +16,7 @@
 ((l, o?) => l + o)(12); // o should be any
 // rest parameters
 ((...numbers) => numbers.every(n => n > 0))(5,6,7);
+((...mixed) => mixed.every(n => !!n))(5,'oops','oh no');
 ((...noNumbers) => noNumbers.some(n => n > 0))();
 ((first, ...rest) => first ? [] : rest.map(n => n > 0))(8,9,10);
 // destructuring parameters (with defaults too!)
@@ -22,5 +24,6 @@
 (({ p = 14 }) => p)({ p : 15 });
 (({ r = 17 } = { r: 18 }) => r)({r : 19});
 (({ u = 22 } = { u: 23 }) => u)();
-
-
+// contextually typed parameters.
+let twelve = (f => f(12))(i => i);
+let eleven = (o => o.a(11))({ a: function(n) { return n; } });