diff --git a/google/cloud/completion_queue.cc b/google/cloud/completion_queue.cc
index 679a69a3969bc..dd43050a08293 100644
--- a/google/cloud/completion_queue.cc
+++ b/google/cloud/completion_queue.cc
@@ -38,7 +38,8 @@ namespace {
 class AsyncTimerFuture : public internal::AsyncGrpcOperation {
  public:
   explicit AsyncTimerFuture(std::unique_ptr<grpc::Alarm> alarm)
-      : alarm_(std::move(alarm)) {}
+      : promise_(/*cancellation_callback=*/[this] { Cancel(); }),
+        alarm_(std::move(alarm)) {}
 
   future<StatusOr<std::chrono::system_clock::time_point>> GetFuture() {
     return promise_.get_future();
diff --git a/google/cloud/completion_queue_test.cc b/google/cloud/completion_queue_test.cc
index a1b78c21040de..f96245cef8ce7 100644
--- a/google/cloud/completion_queue_test.cc
+++ b/google/cloud/completion_queue_test.cc
@@ -330,7 +330,7 @@ TEST(CompletionQueueTest, RunAsync) {
   runner.join();
 }
 
-// Sets up a timer that reschedules itself and verfies we can shut down
+// Sets up a timer that reschedules itself and verifies we can shut down
 // cleanly whether we call `CancelAll()` on the queue first or not.
 namespace {
 void RunAndReschedule(CompletionQueue& cq, bool ok) {
@@ -363,6 +363,35 @@ TEST(CompletionQueueTest, CancelAndShutdownWithReschedulingTimer) {
   t.join();
 }
 
+TEST(CompletionQueueTest, CancelTimerSimple) {
+  CompletionQueue cq;
+  std::thread t([&cq] { cq.Run(); });
+
+  using ms = std::chrono::milliseconds;
+  auto fut = cq.MakeRelativeTimer(ms(20000));
+  fut.cancel();
+  auto tp = fut.get();
+  EXPECT_FALSE(tp.ok()) << ", status=" << tp.status();
+  cq.Shutdown();
+  t.join();
+}
+
+TEST(CompletionQueueTest, CancelTimerContinuation) {
+  CompletionQueue cq;
+  std::thread t([&cq] { cq.Run(); });
+
+  using ms = std::chrono::milliseconds;
+  auto fut = cq.MakeRelativeTimer(ms(20000)).then(
+      [](future<StatusOr<std::chrono::system_clock::time_point>> f) {
+        return f.get().status();
+      });
+  fut.cancel();
+  auto status = fut.get();
+  EXPECT_FALSE(status.ok()) << ", status=" << status;
+  cq.Shutdown();
+  t.join();
+}
+
 }  // namespace
 }  // namespace GOOGLE_CLOUD_CPP_NS
 }  // namespace cloud
diff --git a/google/cloud/future_generic_then_test.cc b/google/cloud/future_generic_then_test.cc
index 2d21bf0a8abb2..785baf65dbf55 100644
--- a/google/cloud/future_generic_then_test.cc
+++ b/google/cloud/future_generic_then_test.cc
@@ -175,6 +175,18 @@ TEST(FutureTestInt, ThenByCopy) {
   EXPECT_FALSE(next.valid());
 }
 
+/// @test Verify the behavior around cancellation.
+TEST(FutureTestInt, CancelThroughContinuation) {
+  bool cancelled = false;
+  promise<int> p0([&cancelled] { cancelled = true; });
+  auto f0 = p0.get_future();
+  auto f1 = f0.then([](future<int> f) { return f.get() * 2; });
+  EXPECT_TRUE(f1.cancel());
+  EXPECT_TRUE(cancelled);
+  p0.set_value(42);
+  EXPECT_EQ(84, f1.get());
+}
+
 // The following tests reference the technical specification:
 //   http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/p0159r0.html
 // The test names match the section and paragraph from the TS.
diff --git a/google/cloud/future_void_then_test.cc b/google/cloud/future_void_then_test.cc
index 4c80916a88708..16ff0e8366e71 100644
--- a/google/cloud/future_void_then_test.cc
+++ b/google/cloud/future_void_then_test.cc
@@ -166,6 +166,18 @@ TEST(FutureTestVoid, ThenByCopy) {
 //   http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/p0159r0.html
 // The test names match the section and paragraph from the TS.
 
+/// @test Verify the behavior around cancellation.
+TEST(FutureTestVoid, CancelThroughContinuation) {
+  bool cancelled = false;
+  promise<void> p0([&cancelled] { cancelled = true; });
+  auto f0 = p0.get_future();
+  auto f1 = f0.then([](future<void>) { return 7; });
+  EXPECT_TRUE(f1.cancel());
+  EXPECT_TRUE(cancelled);
+  p0.set_value();
+  EXPECT_EQ(7, f1.get());
+}
+
 /// @test Verify conformance with section 2.3 of the Concurrency TS.
 TEST(FutureTestVoid, conform_2_3_2_a) {
   // future<void> should have an unwrapping constructor.
diff --git a/google/cloud/internal/future_impl.h b/google/cloud/internal/future_impl.h
index 3b3c3ed6940fa..9c32e5442b64b 100644
--- a/google/cloud/internal/future_impl.h
+++ b/google/cloud/internal/future_impl.h
@@ -69,11 +69,11 @@ class continuation_base {
 class future_shared_state_base {
  public:
   future_shared_state_base() : future_shared_state_base([] {}) {}
-  future_shared_state_base(std::function<void()> cancellation_callback)
+  explicit future_shared_state_base(std::function<void()> cancellation_callback)
       : mu_(),
         cv_(),
         current_state_(state::not_ready),
-        cancellation_callback_(cancellation_callback) {}
+        cancellation_callback_(std::move(cancellation_callback)) {}
   /// Return true if the shared state has a value or an exception.
   bool is_ready() const {
     std::unique_lock<std::mutex> lk(mu_);
@@ -204,6 +204,10 @@ class future_shared_state_base {
     continuation_ = std::move(c);
   }
 
+  std::function<void()> extract_cancellation_callback() {
+    return std::move(cancellation_callback_);
+  }
+
   // Try to cancel the task by invoking the cancellation_callback.
   bool cancel() {
     if (!cancellable()) {
@@ -330,8 +334,8 @@ template <typename T>
 class future_shared_state final : private future_shared_state_base {
  public:
   future_shared_state() : future_shared_state_base(), buffer_() {}
-  future_shared_state(std::function<void()> cancellation_callback)
-      : future_shared_state_base(cancellation_callback), buffer_() {}
+  explicit future_shared_state(std::function<void()> cancellation_callback)
+      : future_shared_state_base(std::move(cancellation_callback)), buffer_() {}
   ~future_shared_state() {
     if (current_state_ == state::has_value) {
       // Recall that state::has_value is a terminal state, once a value is
@@ -345,6 +349,7 @@ class future_shared_state final : private future_shared_state_base {
 
   using future_shared_state_base::abandon;
   using future_shared_state_base::cancel;
+  using future_shared_state_base::extract_cancellation_callback;
   using future_shared_state_base::is_ready;
   using future_shared_state_base::set_continuation;
   using future_shared_state_base::set_exception;
@@ -468,11 +473,12 @@ template <>
 class future_shared_state<void> final : private future_shared_state_base {
  public:
   future_shared_state() : future_shared_state_base() {}
-  future_shared_state(std::function<void()> cancellation_callback)
-      : future_shared_state_base(cancellation_callback) {}
+  explicit future_shared_state(std::function<void()> cancellation_callback)
+      : future_shared_state_base(std::move(cancellation_callback)) {}
 
   using future_shared_state_base::abandon;
   using future_shared_state_base::cancel;
+  using future_shared_state_base::extract_cancellation_callback;
   using future_shared_state_base::is_ready;
   using future_shared_state_base::set_continuation;
   using future_shared_state_base::set_exception;
@@ -666,7 +672,8 @@ struct continuation : public continuation_base {
   continuation(Functor&& f, std::shared_ptr<input_shared_state_t> s)
       : functor(std::move(f)),
         input(std::move(s)),
-        output(std::make_shared<future_shared_state<result_t>>()) {}
+        output(std::make_shared<future_shared_state<result_t>>(
+            input.lock()->extract_cancellation_callback())) {}
 
   continuation(Functor&& f, std::shared_ptr<input_shared_state_t> s,
                std::shared_ptr<output_shared_state_t> o)
@@ -721,7 +728,8 @@ struct unwrapping_continuation : public continuation_base {
       : functor(std::move(f)),
         input(std::move(s)),
         intermediate(),
-        output(std::make_shared<output_shared_state_t>()) {}
+        output(std::make_shared<output_shared_state_t>(
+            input.lock()->extract_cancellation_callback())) {}
 
   void execute() override {
     auto tmp = input.lock();
diff --git a/google/cloud/internal/future_then_impl.h b/google/cloud/internal/future_then_impl.h
index 0cfc81cc3354f..998d14be9df41 100644
--- a/google/cloud/internal/future_then_impl.h
+++ b/google/cloud/internal/future_then_impl.h
@@ -54,9 +54,9 @@ typename internal::then_helper<F, T>::future_t future<T>::then_impl(
       typename internal::then_helper<F, T>::functor_result_t;
   using future_t = typename internal::then_helper<F, T>::future_t;
 
-  // The `shared_state_type` (aka `future_shared_state<T>`) is be written
+  // The `shared_state_type` (aka `future_shared_state<T>`) is written
   // without any reference to the `future<T>` class, otherwise there would
-  // be cycling dependencies between the two classes. We must adapt the
+  // be cyclic dependencies between the two classes. We must adapt the
   // provided functor, which takes a `future<T>` parameter to take a
   // `shared_ptr<shared_state_type` parameter so it can be consumed by the
   // underlying class. Because we need to support C++11, we use a local class