diff --git a/migration/ram.h b/migration/ram.h
index d386f4d641..457bf54b8c 100644
--- a/migration/ram.h
+++ b/migration/ram.h
@@ -46,7 +46,7 @@ int multifd_save_cleanup(Error **errp);
 int multifd_load_setup(void);
 int multifd_load_cleanup(Error **errp);
 bool multifd_recv_all_channels_created(void);
-void multifd_recv_new_channel(QIOChannel *ioc);
+bool multifd_recv_new_channel(QIOChannel *ioc);
 
 uint64_t ram_pagesize_summary(void);
 int ram_save_queue_pages(const char *rbname, ram_addr_t start, ram_addr_t len);
diff --git a/migration/exec.c b/migration/exec.c
index 0bbeb63c97..375d2e1b54 100644
--- a/migration/exec.c
+++ b/migration/exec.c
@@ -49,9 +49,6 @@ static gboolean exec_accept_incoming_migration(QIOChannel *ioc,
 {
     migration_channel_process_incoming(ioc);
     object_unref(OBJECT(ioc));
-    if (!migrate_use_multifd()) {
-        migration_incoming_process();
-    }
     return G_SOURCE_REMOVE;
 }
 
diff --git a/migration/fd.c b/migration/fd.c
index fee34ffdc0..a7c13df4ad 100644
--- a/migration/fd.c
+++ b/migration/fd.c
@@ -49,9 +49,6 @@ static gboolean fd_accept_incoming_migration(QIOChannel *ioc,
 {
     migration_channel_process_incoming(ioc);
     object_unref(OBJECT(ioc));
-    if (!migrate_use_multifd()) {
-        migration_incoming_process();
-    }
     return G_SOURCE_REMOVE;
 }
 
diff --git a/migration/migration.c b/migration/migration.c
index 1e99ec9b7e..b8ed3dcd2f 100644
--- a/migration/migration.c
+++ b/migration/migration.c
@@ -461,7 +461,8 @@ void migration_incoming_process(void)
     qemu_coroutine_enter(co);
 }
 
-void migration_fd_process_incoming(QEMUFile *f)
+/* Returns true if recovered from a paused migration, otherwise false */
+static bool postcopy_try_recover(QEMUFile *f)
 {
     MigrationIncomingState *mis = migration_incoming_get_current();
 
@@ -486,23 +487,40 @@ void migration_fd_process_incoming(QEMUFile *f)
          * that source is ready to reply to page requests.
          */
         qemu_sem_post(&mis->postcopy_pause_sem_dst);
-    } else {
-        /* New incoming migration */
-        migration_incoming_setup(f);
-        migration_incoming_process();
+        return true;
     }
+
+    return false;
 }
 
 void migration_ioc_process_incoming(QIOChannel *ioc)
 {
     MigrationIncomingState *mis = migration_incoming_get_current();
+    QEMUFile *f = qemu_fopen_channel_input(ioc);
+    bool start_migration;
+
+    /* If it's a recovery attempt, we're done */
+    if (postcopy_try_recover(f)) {
+        return;
+    }
 
     if (!mis->from_src_file) {
-        QEMUFile *f = qemu_fopen_channel_input(ioc);
+        /* The first connection (multifd may have multiple) */
         migration_incoming_setup(f);
-        return;
+        /*
+         * Common migration only needs one channel, so we can start
+         * right now.  Multifd needs more than one channel, we wait.
+         */
+        start_migration = !migrate_use_multifd();
+    } else {
+        /* Multiple connections */
+        assert(migrate_use_multifd());
+        start_migration = multifd_recv_new_channel(ioc);
+    }
+
+    if (start_migration) {
+        migration_incoming_process();
     }
-    multifd_recv_new_channel(ioc);
 }
 
 /**
diff --git a/migration/ram.c b/migration/ram.c
index a500015a2f..0d8f38d968 100644
--- a/migration/ram.c
+++ b/migration/ram.c
@@ -871,7 +871,8 @@ bool multifd_recv_all_channels_created(void)
     return thread_count == atomic_read(&multifd_recv_state->count);
 }
 
-void multifd_recv_new_channel(QIOChannel *ioc)
+/* Return true if multifd is ready for the migration, otherwise false */
+bool multifd_recv_new_channel(QIOChannel *ioc)
 {
     MultiFDRecvParams *p;
     Error *local_err = NULL;
@@ -880,7 +881,7 @@ void multifd_recv_new_channel(QIOChannel *ioc)
     id = multifd_recv_initial_packet(ioc, &local_err);
     if (id < 0) {
         multifd_recv_terminate_threads(local_err);
-        return;
+        return false;
     }
 
     p = &multifd_recv_state->params[id];
@@ -888,7 +889,7 @@ void multifd_recv_new_channel(QIOChannel *ioc)
         error_setg(&local_err, "multifd: received id '%d' already setup'",
                    id);
         multifd_recv_terminate_threads(local_err);
-        return;
+        return false;
     }
     p->c = ioc;
     object_ref(OBJECT(ioc));
@@ -897,9 +898,7 @@ void multifd_recv_new_channel(QIOChannel *ioc)
     qemu_thread_create(&p->thread, p->name, multifd_recv_thread, p,
                        QEMU_THREAD_JOINABLE);
     atomic_inc(&multifd_recv_state->count);
-    if (multifd_recv_state->count == migrate_multifd_channels()) {
-        migration_incoming_process();
-    }
+    return multifd_recv_state->count == migrate_multifd_channels();
 }
 
 /**
diff --git a/migration/rdma.c b/migration/rdma.c
index 05aee3d591..0f5ee987c6 100644
--- a/migration/rdma.c
+++ b/migration/rdma.c
@@ -3687,7 +3687,8 @@ static void rdma_accept_incoming_migration(void *opaque)
     }
 
     rdma->migration_started_on_destination = 1;
-    migration_fd_process_incoming(f);
+    migration_incoming_setup(f);
+    migration_incoming_process();
 }
 
 void rdma_start_incoming_migration(const char *host_port, Error **errp)
diff --git a/migration/socket.c b/migration/socket.c
index 3456eb76e9..f4c8174400 100644
--- a/migration/socket.c
+++ b/migration/socket.c
@@ -168,12 +168,7 @@ static void socket_accept_incoming_migration(QIONetListener *listener,
     if (migration_has_all_channels()) {
         /* Close listening socket as its no longer needed */
         qio_net_listener_disconnect(listener);
-
         object_unref(OBJECT(listener));
-
-        if (!migrate_use_multifd()) {
-            migration_incoming_process();
-        }
     }
 }
 
