diff --git a/api_guard/dist/types/index.d.ts b/api_guard/dist/types/index.d.ts
index 18585e7b12..2f610e8800 100644
--- a/api_guard/dist/types/index.d.ts
+++ b/api_guard/dist/types/index.d.ts
@@ -201,8 +201,6 @@ export declare type Head<X extends readonly any[]> = ((...args: X) => any) exten
 
 export declare function identity<T>(x: T): T;
 
-export declare function iif<T>(condition: () => true, trueResult: ObservableInput<T>, falseResult: ObservableInput<any>): Observable<T>;
-export declare function iif<F>(condition: () => false, trueResult: ObservableInput<any>, falseResult: ObservableInput<F>): Observable<F>;
 export declare function iif<T, F>(condition: () => boolean, trueResult: ObservableInput<T>, falseResult: ObservableInput<F>): Observable<T | F>;
 
 export interface InteropObservable<T> {
diff --git a/api_guard/dist/types/operators/index.d.ts b/api_guard/dist/types/operators/index.d.ts
index 3a85ca4d31..fe2b5d0da7 100644
--- a/api_guard/dist/types/operators/index.d.ts
+++ b/api_guard/dist/types/operators/index.d.ts
@@ -130,8 +130,6 @@ export declare function first<T>(predicate: BooleanConstructor): OperatorFunctio
 export declare function first<T, D>(predicate: BooleanConstructor, defaultValue: D): OperatorFunction<T, TruthyTypesOf<T> | D>;
 export declare function first<T, S extends T>(predicate: (value: T, index: number, source: Observable<T>) => value is S, defaultValue?: S): OperatorFunction<T, S>;
 export declare function first<T, S extends T, D>(predicate: (value: T, index: number, source: Observable<T>) => value is S, defaultValue: D): OperatorFunction<T, S | D>;
-export declare function first<T, D>(predicate: (value: T, index: number, source: Observable<T>) => false, defaultValue: D): OperatorFunction<T, D>;
-export declare function first<T>(predicate: (value: T, index: number, source: Observable<T>) => false): OperatorFunction<T, never>;
 export declare function first<T, D = T>(predicate: (value: T, index: number, source: Observable<T>) => boolean, defaultValue?: D): OperatorFunction<T, T | D>;
 
 export declare const flatMap: typeof mergeMap;
@@ -150,8 +148,6 @@ export declare function last<T>(predicate: BooleanConstructor): OperatorFunction
 export declare function last<T, D>(predicate: BooleanConstructor, defaultValue: D): OperatorFunction<T, TruthyTypesOf<T> | D>;
 export declare function last<T, D = T>(predicate?: null, defaultValue?: D): OperatorFunction<T, T | D>;
 export declare function last<T, S extends T>(predicate: (value: T, index: number, source: Observable<T>) => value is S, defaultValue?: S): OperatorFunction<T, S>;
-export declare function last<T, D>(predicate: (value: T, index: number, source: Observable<T>) => false, defaultValue: D): OperatorFunction<T, D>;
-export declare function last<T>(predicate: (value: T, index: number, source: Observable<T>) => false): OperatorFunction<T, never>;
 export declare function last<T, D = T>(predicate: (value: T, index: number, source: Observable<T>) => boolean, defaultValue?: D): OperatorFunction<T, T | D>;
 
 export declare function map<T, R>(project: (value: T, index: number) => R, thisArg?: any): OperatorFunction<T, R>;
@@ -256,7 +252,6 @@ export declare function shareReplay<T>(config: ShareReplayConfig): MonoTypeOpera
 export declare function shareReplay<T>(bufferSize?: number, windowTime?: number, scheduler?: SchedulerLike): MonoTypeOperatorFunction<T>;
 
 export declare function single<T>(predicate: BooleanConstructor): OperatorFunction<T, TruthyTypesOf<T>>;
-export declare function single<T>(predicate: (value: T, index: number, source: Observable<T>) => false): OperatorFunction<T, never>;
 export declare function single<T>(predicate?: (value: T, index: number, source: Observable<T>) => boolean): MonoTypeOperatorFunction<T>;
 
 export declare function skip<T>(count: number): MonoTypeOperatorFunction<T>;
@@ -298,8 +293,6 @@ export declare function takeLast<T>(count: number): MonoTypeOperatorFunction<T>;
 
 export declare function takeUntil<T>(notifier: ObservableInput<any>): MonoTypeOperatorFunction<T>;
 
-export declare function takeWhile<T>(predicate: (value: T, index: number) => false, inclusive: true): MonoTypeOperatorFunction<T>;
-export declare function takeWhile<T>(predicate: (value: T, index: number) => false, inclusive?: false): OperatorFunction<T, never>;
 export declare function takeWhile<T>(predicate: BooleanConstructor): OperatorFunction<T, Exclude<T, Falsy> extends never ? never : T>;
 export declare function takeWhile<T>(predicate: BooleanConstructor, inclusive: false): OperatorFunction<T, Exclude<T, Falsy> extends never ? never : T>;
 export declare function takeWhile<T>(predicate: BooleanConstructor, inclusive: true): MonoTypeOperatorFunction<T>;
diff --git a/spec-dtslint/observables/iif-spec.ts b/spec-dtslint/observables/iif-spec.ts
index 554d4afb44..8fbf38fff0 100644
--- a/spec-dtslint/observables/iif-spec.ts
+++ b/spec-dtslint/observables/iif-spec.ts
@@ -16,10 +16,19 @@ it('should error for incorrect parameters', () => {
 });
 
 it('should infer correctly', () => {
-  const r0 = iif(() => false, a$, b$); // $ExpectType Observable<B>
-  const r1 = iif(() => true, a$, b$); // $ExpectType Observable<A>
+  const r0 = iif(() => false, a$, b$); // $ExpectType Observable<A | B>
+  const r1 = iif(() => true, a$, b$); // $ExpectType Observable<A | B>
   const r2 = iif(randomBoolean, a$, b$); // $ExpectType Observable<A | B>
-  const r3 = iif(() => false, a$, EMPTY); // $ExpectType Observable<never>
-  const r4 = iif(() => true, EMPTY, b$); // $ExpectType Observable<never>
+  const r3 = iif(() => false, a$, EMPTY); // $ExpectType Observable<A>
+  const r4 = iif(() => true, EMPTY, b$); // $ExpectType Observable<B>
   const r5 = iif(randomBoolean, EMPTY, EMPTY); // $ExpectType Observable<never>
 });
+
+
+it('should support inference from a predicate that returns any', () => {
+  function alwaysTrueButReturnsAny(): any {
+    return true;
+  }
+
+  const o$ = iif(alwaysTrueButReturnsAny, a$, b$) // $ExpectType Observable<A | B>
+});
\ No newline at end of file
diff --git a/spec-dtslint/operators/first-spec.ts b/spec-dtslint/operators/first-spec.ts
index 1836b669ee..501ceea0d9 100644
--- a/spec-dtslint/operators/first-spec.ts
+++ b/spec-dtslint/operators/first-spec.ts
@@ -65,4 +65,12 @@ it('should work properly with the Boolean constructor', () => {
   const o3 = of('' as const, 'hi' as const).pipe(first(Boolean)); // $ExpectType Observable<"hi">
   const o4 = of(0 as const, 'hi' as const).pipe(first(Boolean)); // $ExpectType Observable<"hi">
   const o5 = of(0 as const, 'hi' as const, 'what' as const).pipe(first(Boolean)); // $ExpectType Observable<"hi" | "what">
-})
\ No newline at end of file
+});
+
+it('should support inference from a predicate that returns any', () => {
+  function isTruthy(value: number): any {
+    return !!value;
+  }
+
+  const o$ = of(1).pipe(first(isTruthy)); // $ExpectType Observable<number>
+});
\ No newline at end of file
diff --git a/spec-dtslint/operators/last-spec.ts b/spec-dtslint/operators/last-spec.ts
index 1d90c43159..be72063b5d 100644
--- a/spec-dtslint/operators/last-spec.ts
+++ b/spec-dtslint/operators/last-spec.ts
@@ -64,8 +64,8 @@ it('should default D to T with a predicate', () => {
 });
 
 it('should handle predicates that always return false properly', () => {
-  const a = of('foo', 'bar').pipe(last(() => false as const)); // $ExpectType Observable<never>
-  const b = of('foo', 'bar').pipe(last(() => false as const, 1337 as const)); // $ExpectType Observable<1337>
+  const a = of('foo', 'bar').pipe(last(() => false as const)); // $ExpectType Observable<string>
+  const b = of('foo', 'bar').pipe(last(() => false as const, 1337 as const)); // $ExpectType Observable<string | 1337>
 });
 
 it('should handle Boolean constructor properly', () => {
@@ -73,4 +73,12 @@ it('should handle Boolean constructor properly', () => {
   const b = of(0 as const, -0 as const, null, undefined, false as const, '' as const, 0n as const).pipe(last(Boolean, 'test' as const)); // $ExpectType Observable<"test">
   const c = of(0 as const, -0 as const, null, 'hi' as const, undefined, false as const, '' as const, 0n as const).pipe(last(Boolean)); // $ExpectType Observable<"hi">
   const d = of(0 as const, -0 as const, null, 'hi' as const, undefined, false as const, '' as const, 0n as const).pipe(last(Boolean, 'test' as const)); // $ExpectType Observable<"test" | "hi">
-})
\ No newline at end of file
+});
+
+it('should support inference from a predicate that returns any', () => {
+  function isTruthy(value: number): any {
+    return !!value;
+  }
+
+  const o$ = of(1).pipe(last(isTruthy)); // $ExpectType Observable<number>
+});
\ No newline at end of file
diff --git a/spec-dtslint/operators/single-spec.ts b/spec-dtslint/operators/single-spec.ts
index a05b03204c..c564d68f40 100644
--- a/spec-dtslint/operators/single-spec.ts
+++ b/spec-dtslint/operators/single-spec.ts
@@ -39,5 +39,13 @@ it('should handle Boolean constructor properly', () => {
 });
 
 it('should handle predicates that always return false properly', () => {
-  const a = of(1, 2, 3, 4).pipe(single(() => false as const)); // $ExpectType Observable<never>
+  const a = of(1, 2, 3, 4).pipe(single(() => false as const)); // $ExpectType Observable<number>
+});
+
+it('should support inference from a predicate that returns any', () => {
+  function isTruthy(value: number): any {
+    return !!value;
+  }
+
+  const o$ = of(1).pipe(single(isTruthy)); // $ExpectType Observable<number>
 });
\ No newline at end of file
diff --git a/spec-dtslint/operators/takeWhile-spec.ts b/spec-dtslint/operators/takeWhile-spec.ts
index 74cd3ab1f0..f3778f692b 100644
--- a/spec-dtslint/operators/takeWhile-spec.ts
+++ b/spec-dtslint/operators/takeWhile-spec.ts
@@ -27,6 +27,14 @@ it('should properly support Boolean constructor', () => {
 });
 
 it('should properly handle predicates that always return false', () => {
-  const a = of(1, 2, 3).pipe(takeWhile(() => false as const)); // $ExpectType Observable<never>
+  const a = of(1, 2, 3).pipe(takeWhile(() => false as const)); // $ExpectType Observable<number>
   const b = of(1, 2, 3).pipe(takeWhile(() => false as const, true)); // $ExpectType Observable<number>
+});
+
+it('should support inference from a predicate that returns any', () => {
+  function isTruthy(value: number): any {
+    return !!value;
+  }
+
+  const o$ = of(1).pipe(takeWhile(isTruthy)); // $ExpectType Observable<number>
 });
\ No newline at end of file
diff --git a/src/internal/observable/iif.ts b/src/internal/observable/iif.ts
index 7b86ea96c9..672710408e 100644
--- a/src/internal/observable/iif.ts
+++ b/src/internal/observable/iif.ts
@@ -3,12 +3,6 @@ import { Observable } from '../Observable';
 import { defer } from './defer';
 import { ObservableInput } from '../types';
 
-export function iif<T>(condition: () => true, trueResult: ObservableInput<T>, falseResult: ObservableInput<any>): Observable<T>;
-
-export function iif<F>(condition: () => false, trueResult: ObservableInput<any>, falseResult: ObservableInput<F>): Observable<F>;
-
-export function iif<T, F>(condition: () => boolean, trueResult: ObservableInput<T>, falseResult: ObservableInput<F>): Observable<T | F>;
-
 /**
  * Checks a boolean at subscription time, and chooses between one of two observable sources
  *
diff --git a/src/internal/operators/first.ts b/src/internal/operators/first.ts
index 2f09673cea..8334656cd7 100644
--- a/src/internal/operators/first.ts
+++ b/src/internal/operators/first.ts
@@ -19,8 +19,6 @@ export function first<T, S extends T, D>(
   predicate: (value: T, index: number, source: Observable<T>) => value is S,
   defaultValue: D
 ): OperatorFunction<T, S | D>;
-export function first<T, D>(predicate: (value: T, index: number, source: Observable<T>) => false, defaultValue: D): OperatorFunction<T, D>;
-export function first<T>(predicate: (value: T, index: number, source: Observable<T>) => false): OperatorFunction<T, never>;
 export function first<T, D = T>(
   predicate: (value: T, index: number, source: Observable<T>) => boolean,
   defaultValue?: D
diff --git a/src/internal/operators/last.ts b/src/internal/operators/last.ts
index 05040ed37f..2e45e17c1f 100644
--- a/src/internal/operators/last.ts
+++ b/src/internal/operators/last.ts
@@ -15,8 +15,6 @@ export function last<T, S extends T>(
   predicate: (value: T, index: number, source: Observable<T>) => value is S,
   defaultValue?: S
 ): OperatorFunction<T, S>;
-export function last<T, D>(predicate: (value: T, index: number, source: Observable<T>) => false, defaultValue: D): OperatorFunction<T, D>;
-export function last<T>(predicate: (value: T, index: number, source: Observable<T>) => false): OperatorFunction<T, never>;
 export function last<T, D = T>(
   predicate: (value: T, index: number, source: Observable<T>) => boolean,
   defaultValue?: D
diff --git a/src/internal/operators/single.ts b/src/internal/operators/single.ts
index 897db2a9b1..9307086554 100644
--- a/src/internal/operators/single.ts
+++ b/src/internal/operators/single.ts
@@ -9,7 +9,6 @@ import { operate } from '../util/lift';
 import { OperatorSubscriber } from './OperatorSubscriber';
 
 export function single<T>(predicate: BooleanConstructor): OperatorFunction<T, TruthyTypesOf<T>>;
-export function single<T>(predicate: (value: T, index: number, source: Observable<T>) => false): OperatorFunction<T, never>;
 export function single<T>(predicate?: (value: T, index: number, source: Observable<T>) => boolean): MonoTypeOperatorFunction<T>;
 
 /**
diff --git a/src/internal/operators/takeWhile.ts b/src/internal/operators/takeWhile.ts
index 151eac4aaa..fd88c290d5 100644
--- a/src/internal/operators/takeWhile.ts
+++ b/src/internal/operators/takeWhile.ts
@@ -3,8 +3,6 @@ import { OperatorFunction, MonoTypeOperatorFunction, Falsy } from '../types';
 import { operate } from '../util/lift';
 import { OperatorSubscriber } from './OperatorSubscriber';
 
-export function takeWhile<T>(predicate: (value: T, index: number) => false, inclusive: true): MonoTypeOperatorFunction<T>;
-export function takeWhile<T>(predicate: (value: T, index: number) => false, inclusive?: false): OperatorFunction<T, never>;
 export function takeWhile<T>(predicate: BooleanConstructor): OperatorFunction<T, Exclude<T, Falsy> extends never ? never : T>;
 export function takeWhile<T>(
   predicate: BooleanConstructor,