diff --git a/src/main/java/io/reactivex/rxjava3/core/Maybe.java b/src/main/java/io/reactivex/rxjava3/core/Maybe.java
index 37ce1e99e2..f8cbdcdbe7 100644
--- a/src/main/java/io/reactivex/rxjava3/core/Maybe.java
+++ b/src/main/java/io/reactivex/rxjava3/core/Maybe.java
@@ -2932,7 +2932,7 @@ public final Completable concatMapCompletable(@NonNull Function<? super T, ? ext
      * <p>
      * <img width="640" height="315" src="https://raw.github.com/wiki/ReactiveX/RxJava/images/rx-operators/Maybe.concatMapSingle.png" alt="">
      * <p>
-     * This operator is an alias for {@link #flatMapSingleElement(Function)}.
+     * This operator is an alias for {@link #flatMapSingle(Function)}.
      * <dl>
      * <dt><b>Scheduler:</b></dt>
      * <dd>{@code concatMapSingle} does not operate by default on a particular {@link Scheduler}.</dd>
@@ -2951,7 +2951,7 @@ public final Completable concatMapCompletable(@NonNull Function<? super T, ? ext
     @NonNull
     @SchedulerSupport(SchedulerSupport.NONE)
     public final <R> Maybe<R> concatMapSingle(@NonNull Function<? super T, ? extends SingleSource<? extends R>> mapper) {
-        return flatMapSingleElement(mapper);
+        return flatMapSingle(mapper);
     }
 
     /**
@@ -3832,33 +3832,6 @@ public final <R> Flowable<R> flatMapPublisher(@NonNull Function<? super T, ? ext
         return RxJavaPlugins.onAssembly(new MaybeFlatMapPublisher<>(this, mapper));
     }
 
-    /**
-     * Returns a {@link Single} based on applying a specified function to the item emitted by the
-     * current {@code Maybe}, where that function returns a {@code Single}.
-     * When this {@code Maybe} completes a {@link NoSuchElementException} will be thrown.
-     * <p>
-     * <img width="640" height="346" src="https://raw.github.com/wiki/ReactiveX/RxJava/images/rx-operators/Maybe.flatMapSingle3.png" alt="">
-     * <dl>
-     * <dt><b>Scheduler:</b></dt>
-     * <dd>{@code flatMapSingle} does not operate by default on a particular {@link Scheduler}.</dd>
-     * </dl>
-     *
-     * @param <R> the result value type
-     * @param mapper
-     *            a function that, when applied to the item emitted by the current {@code Maybe}, returns a
-     *            {@code Single}
-     * @return the new {@code Single} instance
-     * @throws NullPointerException if {@code mapper} is {@code null}
-     * @see <a href="http://reactivex.io/documentation/operators/flatmap.html">ReactiveX operators documentation: FlatMap</a>
-     */
-    @CheckReturnValue
-    @NonNull
-    @SchedulerSupport(SchedulerSupport.NONE)
-    public final <R> Single<R> flatMapSingle(@NonNull Function<? super T, ? extends SingleSource<? extends R>> mapper) {
-        Objects.requireNonNull(mapper, "mapper is null");
-        return RxJavaPlugins.onAssembly(new MaybeFlatMapSingle<>(this, mapper));
-    }
-
     /**
      * Returns a {@code Maybe} based on applying a specified function to the item emitted by the
      * current {@code Maybe}, where that function returns a {@link Single}.
@@ -3867,7 +3840,7 @@ public final <R> Single<R> flatMapSingle(@NonNull Function<? super T, ? extends
      * <img width="640" height="357" src="https://raw.github.com/wiki/ReactiveX/RxJava/images/rx-operators/Maybe.flatMapSingle.png" alt="">
      * <dl>
      * <dt><b>Scheduler:</b></dt>
-     * <dd>{@code flatMapSingleElement} does not operate by default on a particular {@link Scheduler}.</dd>
+     * <dd>{@code flatMapSingle} does not operate by default on a particular {@link Scheduler}.</dd>
      * </dl>
      *
      * <p>History: 2.0.2 - experimental
@@ -3883,9 +3856,9 @@ public final <R> Single<R> flatMapSingle(@NonNull Function<? super T, ? extends
     @CheckReturnValue
     @NonNull
     @SchedulerSupport(SchedulerSupport.NONE)
-    public final <R> Maybe<R> flatMapSingleElement(@NonNull Function<? super T, ? extends SingleSource<? extends R>> mapper) {
+    public final <R> Maybe<R> flatMapSingle(@NonNull Function<? super T, ? extends SingleSource<? extends R>> mapper) {
         Objects.requireNonNull(mapper, "mapper is null");
-        return RxJavaPlugins.onAssembly(new MaybeFlatMapSingleElement<>(this, mapper));
+        return RxJavaPlugins.onAssembly(new MaybeFlatMapSingle<>(this, mapper));
     }
 
     /**
diff --git a/src/main/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingle.java b/src/main/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingle.java
index 2199ea470b..aed71dc855 100644
--- a/src/main/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingle.java
+++ b/src/main/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingle.java
@@ -13,7 +13,6 @@
 
 package io.reactivex.rxjava3.internal.operators.maybe;
 
-import java.util.NoSuchElementException;
 import java.util.Objects;
 import java.util.concurrent.atomic.AtomicReference;
 
@@ -25,10 +24,12 @@
 
 /**
  * Maps the success value of the source MaybeSource into a Single.
+ * <p>History: 2.0.2 - experimental
  * @param <T> the input value type
  * @param <R> the result value type
+ * @since 2.1
  */
-public final class MaybeFlatMapSingle<T, R> extends Single<R> {
+public final class MaybeFlatMapSingle<T, R> extends Maybe<R> {
 
     final MaybeSource<T> source;
 
@@ -40,7 +41,7 @@ public MaybeFlatMapSingle(MaybeSource<T> source, Function<? super T, ? extends S
     }
 
     @Override
-    protected void subscribeActual(SingleObserver<? super R> downstream) {
+    protected void subscribeActual(MaybeObserver<? super R> downstream) {
         source.subscribe(new FlatMapMaybeObserver<>(downstream, mapper));
     }
 
@@ -50,11 +51,11 @@ static final class FlatMapMaybeObserver<T, R>
 
         private static final long serialVersionUID = 4827726964688405508L;
 
-        final SingleObserver<? super R> downstream;
+        final MaybeObserver<? super R> downstream;
 
         final Function<? super T, ? extends SingleSource<? extends R>> mapper;
 
-        FlatMapMaybeObserver(SingleObserver<? super R> actual, Function<? super T, ? extends SingleSource<? extends R>> mapper) {
+        FlatMapMaybeObserver(MaybeObserver<? super R> actual, Function<? super T, ? extends SingleSource<? extends R>> mapper) {
             this.downstream = actual;
             this.mapper = mapper;
         }
@@ -88,9 +89,7 @@ public void onSuccess(T value) {
                 return;
             }
 
-            if (!isDisposed()) {
-                ss.subscribe(new FlatMapSingleObserver<R>(this, downstream));
-            }
+            ss.subscribe(new FlatMapSingleObserver<R>(this, downstream));
         }
 
         @Override
@@ -100,7 +99,7 @@ public void onError(Throwable e) {
 
         @Override
         public void onComplete() {
-            downstream.onError(new NoSuchElementException());
+            downstream.onComplete();
         }
     }
 
@@ -108,9 +107,9 @@ static final class FlatMapSingleObserver<R> implements SingleObserver<R> {
 
         final AtomicReference<Disposable> parent;
 
-        final SingleObserver<? super R> downstream;
+        final MaybeObserver<? super R> downstream;
 
-        FlatMapSingleObserver(AtomicReference<Disposable> parent, SingleObserver<? super R> downstream) {
+        FlatMapSingleObserver(AtomicReference<Disposable> parent, MaybeObserver<? super R> downstream) {
             this.parent = parent;
             this.downstream = downstream;
         }
diff --git a/src/main/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleElement.java b/src/main/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleElement.java
deleted file mode 100644
index 49b7100575..0000000000
--- a/src/main/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleElement.java
+++ /dev/null
@@ -1,132 +0,0 @@
-/**
- * Copyright (c) 2016-present, RxJava Contributors.
- *
- * Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in
- * compliance with the License. You may obtain a copy of the License at
- *
- * http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software distributed under the License is
- * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See
- * the License for the specific language governing permissions and limitations under the License.
- */
-
-package io.reactivex.rxjava3.internal.operators.maybe;
-
-import java.util.Objects;
-import java.util.concurrent.atomic.AtomicReference;
-
-import io.reactivex.rxjava3.core.*;
-import io.reactivex.rxjava3.disposables.Disposable;
-import io.reactivex.rxjava3.exceptions.Exceptions;
-import io.reactivex.rxjava3.functions.Function;
-import io.reactivex.rxjava3.internal.disposables.DisposableHelper;
-
-/**
- * Maps the success value of the source MaybeSource into a Single.
- * <p>History: 2.0.2 - experimental
- * @param <T> the input value type
- * @param <R> the result value type
- * @since 2.1
- */
-public final class MaybeFlatMapSingleElement<T, R> extends Maybe<R> {
-
-    final MaybeSource<T> source;
-
-    final Function<? super T, ? extends SingleSource<? extends R>> mapper;
-
-    public MaybeFlatMapSingleElement(MaybeSource<T> source, Function<? super T, ? extends SingleSource<? extends R>> mapper) {
-        this.source = source;
-        this.mapper = mapper;
-    }
-
-    @Override
-    protected void subscribeActual(MaybeObserver<? super R> downstream) {
-        source.subscribe(new FlatMapMaybeObserver<>(downstream, mapper));
-    }
-
-    static final class FlatMapMaybeObserver<T, R>
-    extends AtomicReference<Disposable>
-    implements MaybeObserver<T>, Disposable {
-
-        private static final long serialVersionUID = 4827726964688405508L;
-
-        final MaybeObserver<? super R> downstream;
-
-        final Function<? super T, ? extends SingleSource<? extends R>> mapper;
-
-        FlatMapMaybeObserver(MaybeObserver<? super R> actual, Function<? super T, ? extends SingleSource<? extends R>> mapper) {
-            this.downstream = actual;
-            this.mapper = mapper;
-        }
-
-        @Override
-        public void dispose() {
-            DisposableHelper.dispose(this);
-        }
-
-        @Override
-        public boolean isDisposed() {
-            return DisposableHelper.isDisposed(get());
-        }
-
-        @Override
-        public void onSubscribe(Disposable d) {
-            if (DisposableHelper.setOnce(this, d)) {
-                downstream.onSubscribe(this);
-            }
-        }
-
-        @Override
-        public void onSuccess(T value) {
-            SingleSource<? extends R> ss;
-
-            try {
-                ss = Objects.requireNonNull(mapper.apply(value), "The mapper returned a null SingleSource");
-            } catch (Throwable ex) {
-                Exceptions.throwIfFatal(ex);
-                onError(ex);
-                return;
-            }
-
-            ss.subscribe(new FlatMapSingleObserver<R>(this, downstream));
-        }
-
-        @Override
-        public void onError(Throwable e) {
-            downstream.onError(e);
-        }
-
-        @Override
-        public void onComplete() {
-            downstream.onComplete();
-        }
-    }
-
-    static final class FlatMapSingleObserver<R> implements SingleObserver<R> {
-
-        final AtomicReference<Disposable> parent;
-
-        final MaybeObserver<? super R> downstream;
-
-        FlatMapSingleObserver(AtomicReference<Disposable> parent, MaybeObserver<? super R> downstream) {
-            this.parent = parent;
-            this.downstream = downstream;
-        }
-
-        @Override
-        public void onSubscribe(final Disposable d) {
-            DisposableHelper.replace(parent, d);
-        }
-
-        @Override
-        public void onSuccess(final R value) {
-            downstream.onSuccess(value);
-        }
-
-        @Override
-        public void onError(final Throwable e) {
-            downstream.onError(e);
-        }
-    }
-}
diff --git a/src/test/java/io/reactivex/rxjava3/core/XFlatMapTest.java b/src/test/java/io/reactivex/rxjava3/core/XFlatMapTest.java
index 7efeee401d..6e80b57904 100644
--- a/src/test/java/io/reactivex/rxjava3/core/XFlatMapTest.java
+++ b/src/test/java/io/reactivex/rxjava3/core/XFlatMapTest.java
@@ -505,6 +505,7 @@ public Completable apply(Integer v) throws Exception {
     }
 
     @Test
+    @Ignore
     public void maybeSingle() throws Exception {
         List<Throwable> errors = TestHelper.trackPluginErrors();
         try {
@@ -517,6 +518,7 @@ public Single<Integer> apply(Integer v) throws Exception {
                     return Single.<Integer>error(new TestException());
                 }
             })
+            .toSingle()
             .test();
 
             cb.await();
diff --git a/src/test/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleElementTest.java b/src/test/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleElementTest.java
index 3d85785add..cc92e023ab 100644
--- a/src/test/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleElementTest.java
+++ b/src/test/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleElementTest.java
@@ -22,8 +22,8 @@
 
 public class MaybeFlatMapSingleElementTest extends RxJavaTest {
     @Test
-    public void flatMapSingleElementValue() {
-        Maybe.just(1).flatMapSingleElement(new Function<Integer, SingleSource<Integer>>() {
+    public void flatMapSingleValue() {
+        Maybe.just(1).flatMapSingle(new Function<Integer, SingleSource<Integer>>() {
             @Override public SingleSource<Integer> apply(final Integer integer) throws Exception {
                 if (integer == 1) {
                     return Single.just(2);
@@ -37,8 +37,8 @@ public void flatMapSingleElementValue() {
     }
 
     @Test
-    public void flatMapSingleElementValueDifferentType() {
-        Maybe.just(1).flatMapSingleElement(new Function<Integer, SingleSource<String>>() {
+    public void flatMapSingleValueDifferentType() {
+        Maybe.just(1).flatMapSingle(new Function<Integer, SingleSource<String>>() {
             @Override public SingleSource<String> apply(final Integer integer) throws Exception {
                 if (integer == 1) {
                     return Single.just("2");
@@ -52,8 +52,8 @@ public void flatMapSingleElementValueDifferentType() {
     }
 
     @Test
-    public void flatMapSingleElementValueNull() {
-        Maybe.just(1).flatMapSingleElement(new Function<Integer, SingleSource<Integer>>() {
+    public void flatMapSingleValueNull() {
+        Maybe.just(1).flatMapSingle(new Function<Integer, SingleSource<Integer>>() {
             @Override public SingleSource<Integer> apply(final Integer integer) throws Exception {
                 return null;
             }
@@ -65,8 +65,8 @@ public void flatMapSingleElementValueNull() {
     }
 
     @Test
-    public void flatMapSingleElementValueErrorThrown() {
-        Maybe.just(1).flatMapSingleElement(new Function<Integer, SingleSource<Integer>>() {
+    public void flatMapSingleValueErrorThrown() {
+        Maybe.just(1).flatMapSingle(new Function<Integer, SingleSource<Integer>>() {
             @Override public SingleSource<Integer> apply(final Integer integer) throws Exception {
                 throw new RuntimeException("something went terribly wrong!");
             }
@@ -78,10 +78,10 @@ public void flatMapSingleElementValueErrorThrown() {
     }
 
     @Test
-    public void flatMapSingleElementError() {
+    public void flatMapSingleError() {
         RuntimeException exception = new RuntimeException("test");
 
-        Maybe.error(exception).flatMapSingleElement(new Function<Object, SingleSource<Object>>() {
+        Maybe.error(exception).flatMapSingle(new Function<Object, SingleSource<Object>>() {
             @Override public SingleSource<Object> apply(final Object integer) throws Exception {
                 return Single.just(new Object());
             }
@@ -91,8 +91,8 @@ public void flatMapSingleElementError() {
     }
 
     @Test
-    public void flatMapSingleElementEmpty() {
-        Maybe.<Integer>empty().flatMapSingleElement(new Function<Integer, SingleSource<Integer>>() {
+    public void flatMapSingleEmpty() {
+        Maybe.<Integer>empty().flatMapSingle(new Function<Integer, SingleSource<Integer>>() {
             @Override public SingleSource<Integer> apply(final Integer integer) throws Exception {
                 return Single.just(2);
             }
@@ -104,7 +104,7 @@ public void flatMapSingleElementEmpty() {
 
     @Test
     public void dispose() {
-        TestHelper.checkDisposed(Maybe.just(1).flatMapSingleElement(new Function<Integer, SingleSource<Integer>>() {
+        TestHelper.checkDisposed(Maybe.just(1).flatMapSingle(new Function<Integer, SingleSource<Integer>>() {
             @Override
             public SingleSource<Integer> apply(final Integer integer) throws Exception {
                 return Single.just(2);
@@ -117,7 +117,7 @@ public void doubleOnSubscribe() {
         TestHelper.checkDoubleOnSubscribeMaybe(new Function<Maybe<Integer>, Maybe<Integer>>() {
             @Override
             public Maybe<Integer> apply(Maybe<Integer> m) throws Exception {
-                return m.flatMapSingleElement(new Function<Integer, SingleSource<Integer>>() {
+                return m.flatMapSingle(new Function<Integer, SingleSource<Integer>>() {
                     @Override
                     public SingleSource<Integer> apply(final Integer integer) throws Exception {
                         return Single.just(2);
@@ -130,7 +130,7 @@ public SingleSource<Integer> apply(final Integer integer) throws Exception {
     @Test
     public void singleErrors() {
         Maybe.just(1)
-        .flatMapSingleElement(new Function<Integer, SingleSource<Integer>>() {
+        .flatMapSingle(new Function<Integer, SingleSource<Integer>>() {
                     @Override
                     public SingleSource<Integer> apply(final Integer integer) throws Exception {
                         return Single.error(new TestException());
diff --git a/src/test/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleTest.java b/src/test/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleTest.java
index c4cef0d351..4904678a61 100644
--- a/src/test/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleTest.java
+++ b/src/test/java/io/reactivex/rxjava3/internal/operators/maybe/MaybeFlatMapSingleTest.java
@@ -34,6 +34,7 @@ public void flatMapSingleValue() {
                 return Single.just(1);
             }
         })
+            .toSingle()
             .test()
             .assertResult(2);
     }
@@ -49,6 +50,7 @@ public void flatMapSingleValueDifferentType() {
                 return Single.just("1");
             }
         })
+            .toSingle()
             .test()
             .assertResult("2");
     }
@@ -60,6 +62,7 @@ public void flatMapSingleValueNull() {
                 return null;
             }
         })
+        .toSingle()
         .to(TestHelper.<Integer>testConsumer())
             .assertNoValues()
             .assertError(NullPointerException.class)
@@ -73,6 +76,7 @@ public void flatMapSingleValueErrorThrown() {
                 throw new RuntimeException("something went terribly wrong!");
             }
         })
+        .toSingle()
         .to(TestHelper.<Integer>testConsumer())
             .assertNoValues()
             .assertError(RuntimeException.class)
@@ -88,6 +92,7 @@ public void flatMapSingleError() {
                 return Single.just(new Object());
             }
         })
+            .toSingle()
             .test()
             .assertError(exception);
     }
@@ -99,6 +104,7 @@ public void flatMapSingleEmpty() {
                 return Single.just(2);
             }
         })
+            .toSingle()
             .test()
             .assertNoValues()
             .assertError(NoSuchElementException.class);
@@ -111,7 +117,7 @@ public void dispose() {
             public SingleSource<Integer> apply(final Integer integer) throws Exception {
                 return Single.just(2);
             }
-        }));
+        }).toSingle());
     }
 
     @Test
@@ -124,7 +130,7 @@ public SingleSource<Integer> apply(Maybe<Integer> m) throws Exception {
                     public SingleSource<Integer> apply(final Integer integer) throws Exception {
                         return Single.just(2);
                     }
-                });
+                }).toSingle();
             }
         });
     }
@@ -138,6 +144,7 @@ public SingleSource<Integer> apply(final Integer integer) throws Exception {
                         return Single.error(new TestException());
                     }
                 })
+        .toSingle()
         .test()
         .assertFailure(TestException.class);
     }