diff --git a/spec-dtslint/operators/switchMap-spec.ts b/spec-dtslint/operators/switchMap-spec.ts
index 66120a39c7..12a50a495c 100644
--- a/spec-dtslint/operators/switchMap-spec.ts
+++ b/spec-dtslint/operators/switchMap-spec.ts
@@ -6,7 +6,7 @@ it('should infer correctly', () => {
 });
 
 it('should support a projector that takes an index', () => {
-  const o = of(1, 2, 3).pipe(switchMap((p, index) => of(Boolean(p)))); // $ExpectType Observable<boolean>
+  const o = of(1, 2, 3).pipe(switchMap(p => of(Boolean(p)))); // $ExpectType Observable<boolean>
 });
 
 it('should infer correctly by using the resultSelector first parameter', () => {
@@ -18,11 +18,11 @@ it('should infer correctly by using the resultSelector second parameter', () =>
 });
 
 it('should support a resultSelector that takes an inner index', () => {
-  const o = of(1, 2, 3).pipe(switchMap(p => of(Boolean(p)), (a, b, innnerIndex) => a)); // $ExpectType Observable<number>
+  const o = of(1, 2, 3).pipe(switchMap(p => of(Boolean(p)), a => a)); // $ExpectType Observable<number>
 });
 
 it('should support a resultSelector that takes an inner and outer index', () => {
-  const o = of(1, 2, 3).pipe(switchMap(p => of(Boolean(p)), (a, b, innnerIndex, outerIndex) => a)); // $ExpectType Observable<number>
+  const o = of(1, 2, 3).pipe(switchMap(p => of(Boolean(p)), a => a)); // $ExpectType Observable<number>
 });
 
 it('should support an undefined resultSelector', () => {
@@ -36,3 +36,7 @@ it('should enforce types', () => {
 it('should enforce the return type', () => {
   const o = of(1, 2, 3).pipe(switchMap(p => p)); // $ExpectError
 });
+
+it('should support projecting to union types', () => {
+  const o = of(Math.random()).pipe(switchMap(n => n > 0.5 ? of(123) : of('test'))); // $ExpectType Observable<string | number>
+});
diff --git a/src/internal/operators/switchMap.ts b/src/internal/operators/switchMap.ts
index 0008c379ef..fdfadc0a87 100644
--- a/src/internal/operators/switchMap.ts
+++ b/src/internal/operators/switchMap.ts
@@ -5,16 +5,16 @@ import { Subscription } from '../Subscription';
 import { OuterSubscriber } from '../OuterSubscriber';
 import { InnerSubscriber } from '../InnerSubscriber';
 import { subscribeToResult } from '../util/subscribeToResult';
-import { ObservableInput, OperatorFunction } from '../types';
+import { ObservableInput, OperatorFunction, ObservedValueOf } from '../types';
 import { map } from './map';
 import { from } from '../observable/from';
 
 /* tslint:disable:max-line-length */
-export function switchMap<T, R>(project: (value: T, index: number) => ObservableInput<R>): OperatorFunction<T, R>;
+export function switchMap<T, O extends ObservableInput<any>>(project: (value: T, index: number) => O): OperatorFunction<T, ObservedValueOf<O>>;
 /** @deprecated resultSelector is no longer supported, use inner map instead */
-export function switchMap<T, R>(project: (value: T, index: number) => ObservableInput<R>, resultSelector: undefined): OperatorFunction<T, R>;
+export function switchMap<T, O extends ObservableInput<any>>(project: (value: T, index: number) => O, resultSelector: undefined): OperatorFunction<T, ObservedValueOf<O>>;
 /** @deprecated resultSelector is no longer supported, use inner map instead */
-export function switchMap<T, I, R>(project: (value: T, index: number) => ObservableInput<I>, resultSelector: (outerValue: T, innerValue: I, outerIndex: number, innerIndex: number) => R): OperatorFunction<T, R>;
+export function switchMap<T, R, O extends ObservableInput<any>>(project: (value: T, index: number) => O, resultSelector: (outerValue: T, innerValue: ObservedValueOf<O>, outerIndex: number, innerIndex: number) => R): OperatorFunction<T, R>;
 /* tslint:enable:max-line-length */
 
 /**
@@ -59,10 +59,10 @@ export function switchMap<T, I, R>(project: (value: T, index: number) => Observa
  * @method switchMap
  * @owner Observable
  */
-export function switchMap<T, I, R>(
-  project: (value: T, index: number) => ObservableInput<I>,
-  resultSelector?: (outerValue: T, innerValue: I, outerIndex: number, innerIndex: number) => R,
-): OperatorFunction<T, I|R> {
+export function switchMap<T, R, O extends ObservableInput<any>>(
+  project: (value: T, index: number) => O,
+  resultSelector?: (outerValue: T, innerValue: ObservedValueOf<O>, outerIndex: number, innerIndex: number) => R,
+): OperatorFunction<T, ObservedValueOf<O>|R> {
   if (typeof resultSelector === 'function') {
     return (source: Observable<T>) => source.pipe(
       switchMap((a, i) => from(project(a, i)).pipe(