diff --git a/spec/operators/catchError-spec.ts b/spec/operators/catchError-spec.ts
index 9eddb87f40..4dd12f0e20 100644
--- a/spec/operators/catchError-spec.ts
+++ b/spec/operators/catchError-spec.ts
@@ -1,6 +1,6 @@
 import { expect } from 'chai';
-import { concat, defer, Observable, of, throwError, EMPTY, from } from 'rxjs';
-import { catchError, map, mergeMap, takeWhile, delay, take } from 'rxjs/operators';
+import { concat, Observable, of, throwError, EMPTY, from } from 'rxjs';
+import { catchError, map, mergeMap, delay, take, finalize } from 'rxjs/operators';
 import * as sinon from 'sinon';
 import { createObservableInputs } from '../helpers/test-helper';
 import { TestScheduler } from 'rxjs/testing';
@@ -161,31 +161,6 @@ describe('catchError operator', () => {
     });
   });
 
-  it('should stop listening to a synchronous observable when unsubscribed', () => {
-    const sideEffects: number[] = [];
-    const synchronousObservable = concat(
-      defer(() => {
-        sideEffects.push(1);
-        return of(1);
-      }),
-      defer(() => {
-        sideEffects.push(2);
-        return of(2);
-      }),
-      defer(() => {
-        sideEffects.push(3);
-        return of(3);
-      })
-    );
-
-    throwError(new Error('Some error')).pipe(
-      catchError(() => synchronousObservable),
-      takeWhile((x) => x != 2) // unsubscribe at the second side-effect
-    ).subscribe(() => { /* noop */ });
-
-    expect(sideEffects).to.deep.equal([1, 2]);
-  });
-
   it('should catch error and replace it with a hot Observable', () => {
     testScheduler.run(({ hot, expectObservable, expectSubscriptions }) => {
       const e1 = hot('  --a--b--#          ');
@@ -457,7 +432,6 @@ describe('catchError operator', () => {
     );
   });
 
-  // TODO: fix firehose unsubscription
   it('should stop listening to a synchronous observable when unsubscribed', () => {
     const sideEffects: number[] = [];
     const synchronousObservable = new Observable(subscriber => {
@@ -477,4 +451,54 @@ describe('catchError operator', () => {
     expect(sideEffects).to.deep.equal([0, 1, 2]);
   });
 
+  it('should call the cleanup function of the catched observable when the source throws synchronously', () => {
+    let clean = false;
+    const testCleanup$ = new Observable(() => () => {
+      clean = true;
+    });
+
+    const subscription = throwError(new Error('Some error')).pipe(
+      catchError(() => testCleanup$),
+    ).subscribe();
+    expect(clean).to.equal(false);
+
+    subscription.unsubscribe();
+    expect(clean).to.equal(true);
+  });
+
+  it('should not alter the order of the teardown logic of the subscription chain', () => {
+    const logs: any[] = [];
+    const VALUE = 'VALUE';
+    const ERROR = 'ERROR';
+    const COMPLETE = 'COMPLETE';
+    const FINALIZED = 'FINALIZED';
+
+    const source = concat(
+      of(VALUE),
+      throwError(ERROR)
+    ).pipe(
+      finalize(() => {
+        logs.push(FINALIZED);
+      })
+    );
+
+    let hasRetried = false;
+    source.pipe(
+      catchError((err, caught) => {
+        if (hasRetried) {
+          throw err;
+        }
+        hasRetried = true;
+        return caught;
+      })
+    )
+    .subscribe(
+      (value) => { logs.push(value); },
+      (e) => { logs.push(e); },
+      () => { logs.push(COMPLETE); }
+    );
+
+    const expectedLogs = [VALUE, FINALIZED, VALUE, ERROR, FINALIZED];
+    expect(logs).to.deep.equal(expectedLogs);
+  });
 });
diff --git a/src/internal/operators/catchError.ts b/src/internal/operators/catchError.ts
index f793d1b3de..f5e3d8b566 100644
--- a/src/internal/operators/catchError.ts
+++ b/src/internal/operators/catchError.ts
@@ -111,44 +111,29 @@ export function catchError<T, O extends ObservableInput<any>>(
   return (source: Observable<T>) =>
     lift(source, function (this: Subscriber<T>, source: Observable<T>) {
       const subscriber = this;
-      const subscription = new Subscription();
-      let innerSub: Subscription | null = null;
-      let syncUnsub = false;
-      let handledResult: Observable<ObservedValueOf<O>>;
+      let nextSource: Observable<T> | null = null;
+      let subscription: Subscription | null = null;
 
-      const handleError = (err: any) => {
-        try {
-          handledResult = from(selector(err, catchError(selector)(source)));
-        } catch (err) {
-          subscriber.error(err);
-          return;
+      const tryNextSubscription = () => {
+        if (subscription && nextSource && !subscriber.closed) {
+          subscription = nextSource.subscribe(subscriber);
         }
       };
 
-      innerSub = source.subscribe(
+      subscription = source.subscribe(
         new CatchErrorSubscriber(subscriber, (err) => {
-          handleError(err);
-          if (handledResult) {
-            if (innerSub) {
-              innerSub.unsubscribe();
-              innerSub = null;
-              subscription.add(handledResult.subscribe(subscriber));
-            } else {
-              syncUnsub = true;
-            }
+          try {
+            nextSource = from(selector(err, catchError(selector)(source)));
+            tryNextSubscription();
+          } catch (selectorErr) {
+            subscriber.error(selectorErr);
           }
         })
       );
 
-      if (syncUnsub) {
-        innerSub.unsubscribe();
-        innerSub = null;
-        subscription.add(handledResult!.subscribe(subscriber));
-      } else {
-        subscription.add(innerSub);
-      }
+      tryNextSubscription();
 
-      return subscription;
+      return () => subscription!.unsubscribe();
     });
 }