diff --git a/reactor-core/src/main/java/reactor/core/publisher/Mono.java b/reactor-core/src/main/java/reactor/core/publisher/Mono.java
index 7e74853ad0..a0ae691c0d 100644
--- a/reactor-core/src/main/java/reactor/core/publisher/Mono.java
+++ b/reactor-core/src/main/java/reactor/core/publisher/Mono.java
@@ -4319,7 +4319,7 @@ public final Mono<Tuple2<Long, T>> timestamp(Scheduler scheduler) {
 	 * @return a {@link CompletableFuture}
 	 */
 	public final CompletableFuture<T> toFuture() {
-		return subscribeWith(new MonoToCompletableFuture<>());
+		return subscribeWith(new MonoToCompletableFuture<>(false));
 	}
 
 	/**
diff --git a/reactor-core/src/main/java/reactor/core/publisher/MonoToCompletableFuture.java b/reactor-core/src/main/java/reactor/core/publisher/MonoToCompletableFuture.java
index 0c35a57721..7fc6d1ac1a 100644
--- a/reactor-core/src/main/java/reactor/core/publisher/MonoToCompletableFuture.java
+++ b/reactor-core/src/main/java/reactor/core/publisher/MonoToCompletableFuture.java
@@ -27,6 +27,11 @@
 final class MonoToCompletableFuture<T> extends CompletableFuture<T> implements CoreSubscriber<T> {
 
 	final AtomicReference<Subscription> ref = new AtomicReference<>();
+	final boolean cancelSourceOnNext;
+
+	MonoToCompletableFuture(boolean sourceCanEmitMoreThanOnce) {
+		this.cancelSourceOnNext = sourceCanEmitMoreThanOnce;
+	}
 
 	@Override
 	public boolean cancel(boolean mayInterruptIfRunning) {
@@ -55,7 +60,9 @@ public void onNext(T t) {
 		Subscription s = ref.getAndSet(null);
 		if (s != null) {
 			complete(t);
-			s.cancel();
+			if (cancelSourceOnNext) {
+				s.cancel();
+			}
 		}
 		else {
 			Operators.onNextDropped(t, currentContext());
diff --git a/reactor-core/src/test/java/reactor/core/publisher/MonoToCompletableFutureTest.java b/reactor-core/src/test/java/reactor/core/publisher/MonoToCompletableFutureTest.java
index eba73efcc1..88d95a72f7 100644
--- a/reactor-core/src/test/java/reactor/core/publisher/MonoToCompletableFutureTest.java
+++ b/reactor-core/src/test/java/reactor/core/publisher/MonoToCompletableFutureTest.java
@@ -16,10 +16,13 @@
 package reactor.core.publisher;
 
 import java.util.concurrent.CompletableFuture;
+import java.util.concurrent.ExecutionException;
+import java.util.concurrent.atomic.AtomicBoolean;
 
 import org.junit.Test;
 
-import static org.assertj.core.api.AssertionsForClassTypes.assertThat;
+import static org.assertj.core.api.Assertions.assertThat;
+import static org.assertj.core.api.Assertions.assertThatExceptionOfType;
 
 public class MonoToCompletableFutureTest {
 
@@ -31,14 +34,18 @@ public void normal() throws Exception {
 		assertThat(f.get()).isEqualTo(1);
 	}
 
-	@Test(expected = Exception.class)
-	public void error() throws Exception {
+	@Test
+	public void error() {
 		CompletableFuture<Integer> f =
-				Mono.<Integer>error(new Exception("test")).toFuture();
+				Mono.<Integer>error(new IllegalStateException("test")).toFuture();
 
 		assertThat(f.isDone()).isTrue();
 		assertThat(f.isCompletedExceptionally()).isTrue();
-		f.get();
+
+		assertThatExceptionOfType(ExecutionException.class)
+				.isThrownBy(f::get)
+				.withCauseExactlyInstanceOf(IllegalStateException.class)
+				.withMessage("java.lang.IllegalStateException: test");
 	}
 
 	@Test
@@ -47,4 +54,28 @@ public void empty() throws Exception {
 
 		assertThat(f.get()).isNull();
 	}
+
+	@Test
+	public void monoSourceIsntCancelled() {
+		AtomicBoolean flag = new AtomicBoolean();
+
+		assertThat(Mono.just("value")
+		    .doOnCancel(() -> flag.set(true))
+		    .toFuture()
+		).isCompletedWithValue("value");
+		
+		assertThat(flag).as("cancelled").isFalse();
+	}
+
+	@Test
+	public void sourceCanBeCancelledExplicitlyByOnNext() {
+		AtomicBoolean flag = new AtomicBoolean();
+
+		assertThat(Flux.just("value")
+		               .doOnCancel(() -> flag.set(true))
+		               .subscribeWith(new MonoToCompletableFuture<>(true))
+		).isCompletedWithValue("value");
+
+		assertThat(flag).as("cancelled").isTrue();
+	}
 }
\ No newline at end of file