diff --git a/spec-dtslint/operators/reduce-spec.ts b/spec-dtslint/operators/reduce-spec.ts
index 5f31ed75ba..1897fadb58 100644
--- a/spec-dtslint/operators/reduce-spec.ts
+++ b/spec-dtslint/operators/reduce-spec.ts
@@ -1,4 +1,4 @@
-import { of, Observable } from 'rxjs';
+import { of, OperatorFunction } from 'rxjs';
 import { reduce } from 'rxjs/operators';
 
 it('should enforce parameter', () => {
@@ -29,3 +29,29 @@ it('should accept seed parameter of a different type', () => {
   const bv: { [key: string]: string } = {};
   const b = of(1, 2, 3).pipe(reduce((x, y, z) => ({ ...x, [y]: y.toString() }), bv)); // $ExpectType Observable<{ [key: string]: string; }>
 });
+
+it('should act appropriately with no seed', () => {
+  // Because an observable of one value will just pass that value directly through the reducer,
+  // the below could be a number or a string.
+  const a = of(1, 2, 3).pipe(reduce((a: any, v) => '' + v)); // $ExpectType Observable<string | number>
+  const b = of(1, 2, 3).pipe(reduce((a, v) => v)); // $ExpectType Observable<number>
+  const c = of(1, 2, 3).pipe(reduce(() => {})); // $ExpectType Observable<number | void>
+});
+
+it('should act appropriately with a seed', () => {
+  const a = of(1, 2, 3).pipe(reduce((a, v) => a + v, '')); // $ExpectType Observable<string>
+  const b = of(1, 2, 3).pipe(reduce((a, v) => a + v, 0)); // $ExpectType Observable<number>
+  const c = of(1, 2, 3).pipe(reduce((a, v) => a + 1, [])); // $ExpectError
+});
+
+it('should infer types properly from arguments', () => {
+  function toArrayReducer(arr: number[], item: number, index: number): number[] {
+    if (index === 0) {
+      return [item];
+    }
+    arr.push(item);
+    return arr;
+  }
+
+  const a = reduce(toArrayReducer, [] as number[]); // $ExpectType OperatorFunction<number, number[]>
+});
diff --git a/spec-dtslint/operators/scan-spec.ts b/spec-dtslint/operators/scan-spec.ts
index f5e73bf114..553813f98f 100644
--- a/spec-dtslint/operators/scan-spec.ts
+++ b/spec-dtslint/operators/scan-spec.ts
@@ -29,3 +29,29 @@ it('should accept seed parameter of a different type', () => {
   const bv: { [key: string]: string } = {};
   const b = of(1, 2, 3).pipe(scan((x, y, z) => ({ ...x, [y]: y.toString() }), bv)); // $ExpectType Observable<{ [key: string]: string; }>
 });
+
+it('should act appropriately with no seed', () => {
+  // Because an observable of one value will just pass that value directly through the reducer,
+  // the below could be a number or a string.
+  const a = of(1, 2, 3).pipe(scan((a: any, v) => '' + v)); // $ExpectType Observable<string | number>
+  const b = of(1, 2, 3).pipe(scan((a, v) => v)); // $ExpectType Observable<number>
+  const c = of(1, 2, 3).pipe(scan(() => {})); // $ExpectType Observable<number | void>
+});
+
+it('should act appropriately with a seed', () => {
+  const a = of(1, 2, 3).pipe(scan((a, v) => a + v, '')); // $ExpectType Observable<string>
+  const b = of(1, 2, 3).pipe(scan((a, v) => a + v, 0)); // $ExpectType Observable<number>
+  const c = of(1, 2, 3).pipe(scan((a, v) => a + 1, [])); // $ExpectError
+});
+
+it('should infer types properly from arguments', () => {
+  function toArrayReducer(arr: number[], item: number, index: number): number[] {
+    if (index === 0) {
+      return [item];
+    }
+    arr.push(item);
+    return arr;
+  }
+
+  const a = scan(toArrayReducer, [] as number[]); // $ExpectType OperatorFunction<number, number[]>
+});
diff --git a/spec/operators/reduce-spec.ts b/spec/operators/reduce-spec.ts
index 4cbea42efc..1823202ef0 100644
--- a/spec/operators/reduce-spec.ts
+++ b/spec/operators/reduce-spec.ts
@@ -193,7 +193,7 @@ describe('reduce operator', () => {
       throw 'error';
     };
 
-    expectObservable(e1.pipe(reduce<string>(reduceFunction, seed))).toBe(expected);
+    expectObservable(e1.pipe(reduce(reduceFunction, seed))).toBe(expected);
     expectSubscriptions(e1.subscriptions).toBe(e1subs);
   });
 
@@ -289,105 +289,4 @@ describe('reduce operator', () => {
     expectObservable(e1.pipe(reduce(reduceFunction))).toBe(expected);
     expectSubscriptions(e1.subscriptions).toBe(e1subs);
   });
-
-  type('should accept array typed reducers', () => {
-    let a: Observable<{ a: number; b: string }>;
-    a.pipe(reduce((acc, value) => acc.concat(value), []));
-  });
-
-  type('should accept T typed reducers', () => {
-    let a: Observable<{ a: number; b: string }>;
-    const reduced = a.pipe(reduce((acc, value) => {
-      value.a = acc.a;
-      value.b = acc.b;
-      return acc;
-    }));
-
-    reduced.subscribe(r => {
-      r.a.toExponential();
-      r.b.toLowerCase();
-    });
-  });
-
-  type('should accept T typed reducers when T is an array', () => {
-    let a: Observable<number[]>;
-    const reduced = a.pipe(reduce((acc, value) => {
-      return acc.concat(value);
-    }, []));
-
-    reduced.subscribe(rs => {
-      rs[0].toExponential();
-    });
-  });
-
-  type('should accept R typed reduces when R is an array of T', () => {
-    let a: Observable<number>;
-    const reduced = a.pipe(reduce((acc, value) => {
-      acc.push(value);
-      return acc;
-    }, []));
-
-    reduced.subscribe(rs => {
-      rs[0].toExponential();
-    });
-  });
-
-  type('should accept R typed reducers when R is assignable to T', () => {
-    let a: Observable<{ a?: number; b?: string }>;
-    const reduced = a.pipe(reduce((acc, value) => {
-      value.a = acc.a;
-      value.b = acc.b;
-      return acc;
-    }, {} as { a?: number; b?: string }));
-
-    reduced.subscribe(r => {
-      r.a.toExponential();
-      r.b.toLowerCase();
-    });
-  });
-
-  type('should accept R typed reducers when R is not assignable to T', () => {
-    let a: Observable<{ a: number; b: string }>;
-    const seed = {
-      as: [1],
-      bs: ['a']
-    };
-    const reduced = a.pipe(reduce((acc, value: {a: number, b: string}) => {
-      acc.as.push(value.a);
-      acc.bs.push(value.b);
-      return acc;
-    }, seed));
-
-    reduced.subscribe(r => {
-      r.as[0].toExponential();
-      r.bs[0].toLowerCase();
-    });
-  });
-
-  type('should accept R typed reducers and reduce to type R', () => {
-    let a: Observable<{ a: number; b: string }>;
-    const reduced = a.pipe(reduce<{ a?: number; b?: string }>((acc, value) => {
-      value.a = acc.a;
-      value.b = acc.b;
-      return acc;
-    }, {}));
-
-    reduced.subscribe(r => {
-      r.a.toExponential();
-      r.b.toLowerCase();
-    });
-  });
-
-  type('should accept array of R typed reducers and reduce to array of R', () => {
-    let a: Observable<number>;
-    const reduced = a.pipe(reduce<number, string[]>((acc, cur) => {
-      console.log(acc);
-      acc.push(cur.toString());
-      return acc;
-    }, [] as string[]));
-
-    reduced.subscribe(rs => {
-      rs[0].toLowerCase();
-    });
-  });
 });
diff --git a/spec/operators/scan-spec.ts b/spec/operators/scan-spec.ts
index 66f4e2d9eb..08b3d8d607 100644
--- a/spec/operators/scan-spec.ts
+++ b/spec/operators/scan-spec.ts
@@ -227,27 +227,4 @@ describe('scan operator', () => {
     expectObservable(scanObs).toBe(expected, values);
     expectSubscriptions(e1.subscriptions).toBe(e1subs);
   });
-
-  type('should accept array typed reducers', () => {
-    let a: Observable<{ a: number; b: string }>;
-    a.pipe(scan((acc, value) => acc.concat(value), []));
-  });
-
-  type('should accept T typed reducers', () => {
-    let a: Observable<{ a?: number; b?: string }>;
-    a.pipe(scan((acc, value) => {
-      value.a = acc.a;
-      value.b = acc.b;
-      return acc;
-    }, {} as { a?: number; b?: string }));
-  });
-
-  type('should accept R typed reducers', () => {
-    let a: Observable<{ a: number; b: string }>;
-    a.pipe(scan<{ a?: number; b?: string }>((acc, value) => {
-      value.a = acc.a;
-      value.b = acc.b;
-      return acc;
-    }, {}));
-  });
 });
diff --git a/src/internal/operators/reduce.ts b/src/internal/operators/reduce.ts
index 6039fdb123..b044e9283f 100644
--- a/src/internal/operators/reduce.ts
+++ b/src/internal/operators/reduce.ts
@@ -2,13 +2,13 @@ import { Observable } from '../Observable';
 import { scan } from './scan';
 import { takeLast } from './takeLast';
 import { defaultIfEmpty } from './defaultIfEmpty';
-import { OperatorFunction, MonoTypeOperatorFunction } from '../types';
+import { OperatorFunction } from '../types';
 import { pipe } from '../util/pipe';
 
 /* tslint:disable:max-line-length */
-export function reduce<T, R>(accumulator: (acc: R, value: T, index: number) => R, seed: R): OperatorFunction<T, R>;
-export function reduce<T>(accumulator: (acc: T, value: T, index: number) => T, seed?: T): MonoTypeOperatorFunction<T>;
-export function reduce<T, R>(accumulator: (acc: R, value: T, index: number) => R): OperatorFunction<T, R>;
+export function reduce<V, A = V>(accumulator: (acc: A|V, value: V, index: number) => A): OperatorFunction<V, V|A>;
+export function reduce<V, A>(accumulator: (acc: A, value: V, index: number) => A, seed: A): OperatorFunction<V, A>;
+export function reduce<V, A, S = A>(accumulator: (acc: A|S, value: V, index: number) => A, seed: S): OperatorFunction<V, A>;
 /* tslint:enable:max-line-length */
 
 /**
@@ -54,28 +54,32 @@ export function reduce<T, R>(accumulator: (acc: R, value: T, index: number) => R
  * @see {@link mergeScan}
  * @see {@link scan}
  *
- * @param {function(acc: R, value: T, index: number): R} accumulator The accumulator function
+ * @param {function(acc: A, value: V, index: number): A} accumulator The accumulator function
  * called on each source value.
- * @param {R} [seed] The initial accumulation value.
- * @return {Observable<R>} An Observable that emits a single value that is the
+ * @param {A} [seed] The initial accumulation value.
+ * @return {Observable<A>} An Observable that emits a single value that is the
  * result of accumulating the values emitted by the source Observable.
  * @method reduce
  * @owner Observable
  */
-export function reduce<T, R>(accumulator: (acc: T | R, value: T, index?: number) => T | R, seed?: T | R): OperatorFunction<T, T | R> {
+export function reduce<V, A>(accumulator: (acc: V | A, value: V, index?: number) => A, seed?: any): OperatorFunction<V, V | A> {
   // providing a seed of `undefined` *should* be valid and trigger
   // hasSeed! so don't use `seed !== undefined` checks!
   // For this reason, we have to check it here at the original call site
   // otherwise inside Operator/Subscriber we won't know if `undefined`
   // means they didn't provide anything or if they literally provided `undefined`
   if (arguments.length >= 2) {
-    return function reduceOperatorFunctionWithSeed(source: Observable<T>): Observable<T | R> {
-      return pipe(scan(accumulator, seed), takeLast(1), defaultIfEmpty(seed))(source);
+    return function reduceOperatorFunctionWithSeed(source: Observable<V>): Observable<V | A> {
+      return pipe(
+        scan(accumulator, seed),
+        takeLast(1),
+        defaultIfEmpty(seed),
+      )(source);
     };
   }
-  return function reduceOperatorFunction(source: Observable<T>): Observable<T | R> {
+  return function reduceOperatorFunction(source: Observable<V>): Observable<V | A> {
     return pipe(
-      scan<T, T | R>((acc, value, index) => accumulator(acc, value, index + 1)),
+      scan<V, V | A>((acc, value, index) => accumulator(acc, value, index + 1)),
       takeLast(1),
     )(source);
   };
diff --git a/src/internal/operators/scan.ts b/src/internal/operators/scan.ts
index a1eb511e40..6ef11d0cf8 100644
--- a/src/internal/operators/scan.ts
+++ b/src/internal/operators/scan.ts
@@ -1,12 +1,12 @@
 import { Operator } from '../Operator';
 import { Observable } from '../Observable';
 import { Subscriber } from '../Subscriber';
-import { OperatorFunction, MonoTypeOperatorFunction } from '../types';
+import { OperatorFunction, TeardownLogic } from '../types';
 
 /* tslint:disable:max-line-length */
-export function scan<T, R>(accumulator: (acc: R, value: T, index: number) => R, seed: R): OperatorFunction<T, R>;
-export function scan<T>(accumulator: (acc: T, value: T, index: number) => T, seed?: T): MonoTypeOperatorFunction<T>;
-export function scan<T, R>(accumulator: (acc: R, value: T, index: number) => R): OperatorFunction<T, R>;
+export function scan<V, A = V>(accumulator: (acc: A|V, value: V, index: number) => A): OperatorFunction<V, V|A>;
+export function scan<V, A>(accumulator: (acc: A, value: V, index: number) => A, seed: A): OperatorFunction<V, A>;
+export function scan<V, A, S>(accumulator: (acc: A|S, value: V, index: number) => A, seed: S): OperatorFunction<V, A>;
 /* tslint:enable:max-line-length */
 
 /**
@@ -45,14 +45,14 @@ export function scan<T, R>(accumulator: (acc: R, value: T, index: number) => R):
  * @see {@link mergeScan}
  * @see {@link reduce}
  *
- * @param {function(acc: R, value: T, index: number): R} accumulator
+ * @param {function(acc: A, value: V, index: number): A} accumulator
  * The accumulator function called on each source value.
- * @param {T|R} [seed] The initial accumulation value.
- * @return {Observable<R>} An observable of the accumulated values.
+ * @param {V|A} [seed] The initial accumulation value.
+ * @return {Observable<A>} An observable of the accumulated values.
  * @method scan
  * @owner Observable
  */
-export function scan<T, R>(accumulator: (acc: R, value: T, index: number) => R, seed?: T | R): OperatorFunction<T, R> {
+export function scan<V, A, S>(accumulator: (acc: V|A|S, value: V, index: number) => A, seed?: S): OperatorFunction<V, V|A> {
   let hasSeed = false;
   // providing a seed of `undefined` *should* be valid and trigger
   // hasSeed! so don't use `seed !== undefined` checks!
@@ -63,15 +63,15 @@ export function scan<T, R>(accumulator: (acc: R, value: T, index: number) => R,
     hasSeed = true;
   }
 
-  return function scanOperatorFunction(source: Observable<T>): Observable<R> {
+  return function scanOperatorFunction(source: Observable<V>) {
     return source.lift(new ScanOperator(accumulator, seed, hasSeed));
   };
 }
 
-class ScanOperator<T, R> implements Operator<T, R> {
-  constructor(private accumulator: (acc: R, value: T, index: number) => R, private seed?: T | R, private hasSeed: boolean = false) {}
+class ScanOperator<V, A, S> implements Operator<V, A> {
+  constructor(private accumulator: (acc: V|A|S, value: V, index: number) => A, private seed?: S, private hasSeed: boolean = false) {}
 
-  call(subscriber: Subscriber<R>, source: any): any {
+  call(subscriber: Subscriber<A>, source: any): TeardownLogic {
     return source.subscribe(new ScanSubscriber(subscriber, this.accumulator, this.seed, this.hasSeed));
   }
 }
@@ -81,41 +81,31 @@ class ScanOperator<T, R> implements Operator<T, R> {
  * @ignore
  * @extends {Ignored}
  */
-class ScanSubscriber<T, R> extends Subscriber<T> {
+class ScanSubscriber<V, A> extends Subscriber<V> {
   private index: number = 0;
 
-  get seed(): T | R {
-    return this._seed;
-  }
-
-  set seed(value: T | R) {
-    this.hasSeed = true;
-    this._seed = value;
-  }
-
-  constructor(destination: Subscriber<R>, private accumulator: (acc: R, value: T, index: number) => R, private _seed: T | R,
-              private hasSeed: boolean) {
+  constructor(destination: Subscriber<A>, private accumulator: (acc: V|A, value: V, index: number) => A, private _state: any,
+              private _hasState: boolean) {
     super(destination);
   }
 
-  protected _next(value: T): void {
-    if (!this.hasSeed) {
-      this.seed = value;
-      this.destination.next(value);
+  protected _next(value: V): void {
+    const { destination } = this;
+    if (!this._hasState) {
+      this._state = value;
+      this._hasState = true;
+      destination.next(value);
     } else {
-      return this._tryNext(value);
-    }
-  }
-
-  private _tryNext(value: T): void {
-    const index = this.index++;
-    let result: any;
-    try {
-      result = this.accumulator(<R>this.seed, value, index);
-    } catch (err) {
-      this.destination.error(err);
+      const index = this.index++;
+      let result: A;
+      try {
+        result = this.accumulator(this._state, value, index);
+      } catch (err) {
+        destination.error(err);
+        return;
+      }
+      this._state = result;
+      destination.next(result);
     }
-    this.seed = result;
-    this.destination.next(result);
   }
 }
diff --git a/src/internal/operators/toArray.ts b/src/internal/operators/toArray.ts
index 40d05601c3..0a5f59a434 100644
--- a/src/internal/operators/toArray.ts
+++ b/src/internal/operators/toArray.ts
@@ -1,7 +1,7 @@
 import { reduce } from './reduce';
 import { OperatorFunction } from '../types';
 
-function toArrayReducer<T>(arr: T[], item: T, index: number) {
+function toArrayReducer<T>(arr: T[], item: T, index: number): T[] {
   if (index === 0) {
     return [item];
   }