diff --git a/libs/pika/async_mpi/include/pika/async_mpi/dispatch_mpi.hpp b/libs/pika/async_mpi/include/pika/async_mpi/dispatch_mpi.hpp
index a1bc641e1..52a4c2eca 100644
--- a/libs/pika/async_mpi/include/pika/async_mpi/dispatch_mpi.hpp
+++ b/libs/pika/async_mpi/include/pika/async_mpi/dispatch_mpi.hpp
@@ -158,18 +158,8 @@ namespace pika::mpi::experimental::detail {
                                         mpi::exception(status, "dispatch mpi")));
                                 return;
                             }
-                            // early poll just in case the request completed immediately
-                            if (poll_request(request))
-                            {
-#ifdef PIKA_HAVE_APEX
-                                apex::scoped_timer apex_invoke("pika::mpi::trigger");
-#endif
-                                PIKA_DETAIL_DP(mpi_tran<7>,
-                                    debug(
-                                        str<>("dispatch_mpi_recv"), "eager poll ok", ptr(request)));
-                                ex::set_value(PIKA_MOVE(r.op_state.receiver), MPI_REQUEST_NULL);
-                            }
-                            else { ex::set_value(PIKA_MOVE(r.op_state.receiver), request); }
+
+                            ex::set_value(PIKA_MOVE(r.op_state.receiver), request);
                         },
                         [&](std::exception_ptr ep) {
                             ex::set_error(PIKA_MOVE(r.op_state.receiver), PIKA_MOVE(ep));
diff --git a/libs/pika/async_mpi/include/pika/async_mpi/transform_mpi.hpp b/libs/pika/async_mpi/include/pika/async_mpi/transform_mpi.hpp
index 7472b6925..cf7a516f9 100644
--- a/libs/pika/async_mpi/include/pika/async_mpi/transform_mpi.hpp
+++ b/libs/pika/async_mpi/include/pika/async_mpi/transform_mpi.hpp
@@ -52,7 +52,6 @@ namespace pika::mpi::experimental {
             using pika::execution::experimental::continues_on;
             using pika::execution::experimental::just;
             using pika::execution::experimental::let_value;
-            using pika::execution::experimental::unique_any_sender;
             using pika::execution::experimental::unpack;
 
             // get mpi completion mode settings
@@ -64,35 +63,40 @@ namespace pika::mpi::experimental {
                 execution::thread_priority::boost :
                 execution::thread_priority::normal;
 
-            auto completion_snd = [=](MPI_Request request) -> unique_any_sender<> {
-                if (!completions_inline)    // not inline : a transfer is required
+            if (completions_inline)
+            {
+                auto f_completion = [mode, f = std::forward<F>(f)](auto&... args) mutable {
+                    return just(std::forward_as_tuple(args...)) | unpack() |
+                        dispatch_mpi(std::move(f)) | trigger_mpi(mode);
+                };
+
+                if (requests_inline)
                 {
-                    if (request == MPI_REQUEST_NULL)
-                    {
-                        return ex::schedule(default_pool_scheduler(p));
-                    }
-                    return just(request) | trigger_mpi(mode) |
-                        ex::continues_on(default_pool_scheduler(p));
+                    return std::forward<Sender>(sender) | let_value(std::move(f_completion));
+                }
+                else
+                {
+                    return std::forward<Sender>(sender) | continues_on(mpi_pool_scheduler(p)) |
+                        let_value(std::move(f_completion));
                 }
-                if (request == MPI_REQUEST_NULL) { return just(); }
-                return just(request) | trigger_mpi(mode);
-            };
-
-            if (requests_inline)
-            {
-                return std::forward<Sender>(sender) |
-                    let_value([=, f = std::forward<F>(f)](auto&... args) mutable {
-                        return just(std::forward_as_tuple(args...)) | ex::unpack() |
-                            dispatch_mpi(std::move(f)) | let_value(completion_snd);
-                    });
             }
             else
             {
-                return std::forward<Sender>(sender) | continues_on(mpi_pool_scheduler(p)) |
-                    let_value([=, f = std::forward<F>(f)](auto&... args) mutable {
-                        return just(std::forward_as_tuple(args...)) | ex::unpack() |
-                            dispatch_mpi(std::move(f)) | let_value(completion_snd);
-                    });
+                auto f_completion = [mode, p, f = std::forward<F>(f)](auto&... args) mutable {
+                    return just(std::forward_as_tuple(args...)) | unpack() |
+                        dispatch_mpi(std::move(f)) | trigger_mpi(mode) |
+                        continues_on(default_pool_scheduler(p));
+                };
+
+                if (requests_inline)
+                {
+                    return std::forward<Sender>(sender) | let_value(std::move(f_completion));
+                }
+                else
+                {
+                    return std::forward<Sender>(sender) | continues_on(mpi_pool_scheduler(p)) |
+                        let_value(std::move(f_completion));
+                }
             }
         }
 
diff --git a/libs/pika/async_mpi/include/pika/async_mpi/trigger_mpi.hpp b/libs/pika/async_mpi/include/pika/async_mpi/trigger_mpi.hpp
index b466073b7..d80e237bd 100644
--- a/libs/pika/async_mpi/include/pika/async_mpi/trigger_mpi.hpp
+++ b/libs/pika/async_mpi/include/pika/async_mpi/trigger_mpi.hpp
@@ -119,9 +119,14 @@ namespace pika::mpi::experimental::detail {
                 {
                     auto r = PIKA_MOVE(*this);
 
-                    // early exit check
-                    if (request == MPI_REQUEST_NULL)
+                    // early poll just in case the request completed immediately
+                    if (poll_request(request))
                     {
+#ifdef PIKA_HAVE_APEX
+                        apex::scoped_timer apex_invoke("pika::mpi::trigger");
+#endif
+                        PIKA_DETAIL_DP(mpi_tran<7>,
+                            debug(str<>("trigger_mpi_recv"), "eager poll ok", ptr(request)));
                         ex::set_value(PIKA_MOVE(r.op_state.receiver));
                         return;
                     }