diff --git a/tests/31sync/15lazy-members.pl b/tests/31sync/15lazy-members.pl
index fb8113189..9e1ffebbd 100644
--- a/tests/31sync/15lazy-members.pl
+++ b/tests/31sync/15lazy-members.pl
@@ -74,6 +74,11 @@
          matrix_create_room_synced( $alice );
       })->then( sub {
          ( $room_id ) = @_;
+         matrix_put_room_state( $alice, $room_id,
+            type    => "m.room.name",
+            content => { name => "A room name" },
+         );
+      })->then( sub {
          matrix_join_room( $bob, $room_id );
       })->then( sub {
          matrix_join_room( $charlie, $room_id );
@@ -136,6 +141,11 @@
          matrix_create_room_synced( $alice );
       })->then( sub {
          ( $room_id ) = @_;
+         matrix_put_room_state( $alice, $room_id,
+            type    => "m.room.name",
+            content => { name => "A room name" },
+         );
+      })->then( sub {
          matrix_join_room( $bob, $room_id );
       })->then( sub {
          matrix_join_room( $charlie, $room_id );
@@ -200,6 +210,11 @@
          matrix_create_room_synced( $alice );
       })->then( sub {
          ( $room_id ) = @_;
+         matrix_put_room_state( $alice, $room_id,
+            type    => "m.room.name",
+            content => { name => "A room name" },
+         );
+      })->then( sub {
          matrix_join_room( $bob, $room_id );
       })->then( sub {
          matrix_join_room( $charlie, $room_id );
@@ -279,6 +294,11 @@
          matrix_create_room_synced( $alice );
       })->then( sub {
          ( $room_id ) = @_;
+         matrix_put_room_state( $alice, $room_id,
+            type    => "m.room.name",
+            content => { name => "A room name" },
+         );
+      })->then( sub {
          matrix_join_room( $bob, $room_id );
       })->then( sub {
          matrix_join_room( $charlie, $room_id );
@@ -358,6 +378,11 @@
          matrix_create_room_synced( $alice );
       })->then( sub {
          ( $room_id ) = @_;
+         matrix_put_room_state( $alice, $room_id,
+            type    => "m.room.name",
+            content => { name => "A room name" },
+         );
+      })->then( sub {
          matrix_join_room( $bob, $room_id );
       })->then( sub {
          matrix_join_room( $charlie, $room_id );
diff --git a/tests/31sync/16room-summary.pl b/tests/31sync/16room-summary.pl
new file mode 100644
index 000000000..d0ef365f7
--- /dev/null
+++ b/tests/31sync/16room-summary.pl
@@ -0,0 +1,140 @@
+use Future::Utils qw( repeat );
+
+test "Unnamed room comes with a name summary",
+   requires => [ local_user_fixtures( 3 ),
+                 qw( can_sync ) ],
+
+   check => sub {
+      my ( $alice, $bob, $charlie ) = @_;
+
+      my ( $filter_id, $room_id );
+
+      matrix_create_filter( $alice, {
+         room => {
+            state => {
+               lazy_load_members => JSON::true
+            },
+         }
+      } )->then( sub {
+         ( $filter_id ) = @_;
+
+         matrix_create_room_synced( $alice );
+      })->then( sub {
+         ( $room_id ) = @_;
+         matrix_join_room_synced( $bob, $room_id );
+      })->then( sub {
+         matrix_join_room( $charlie, $room_id );
+      })->then( sub {
+         matrix_sync( $alice, filter => $filter_id );
+      })->then( sub {
+         my ( $body ) = @_;
+         log_if_fail ( "sync response:", $body->{rooms}{join}{$room_id} );
+         my $summary = $body->{rooms}{join}{$room_id}{summary};
+         assert_deeply_eq( $summary, {
+            'm.joined_member_count' => 3,
+            'm.invited_member_count' => 0,
+            'm.heroes' => [
+               $bob->user_id,
+               $charlie->user_id,
+            ]
+         });
+         Future->done(1);
+      });
+   };
+
+test "Named room comes with just joined member count summary",
+   requires => [ local_user_fixtures( 3 ),
+                 qw( can_sync ) ],
+
+   check => sub {
+      my ( $alice, $bob, $charlie ) = @_;
+
+      my ( $filter_id, $room_id );
+
+      matrix_create_filter( $alice, {
+         room => {
+            state => {
+               lazy_load_members => JSON::true
+            },
+         }
+      } )->then( sub {
+         ( $filter_id ) = @_;
+
+         matrix_create_room_synced( $alice );
+      })->then( sub {
+         ( $room_id ) = @_;
+         matrix_put_room_state( $alice, $room_id,
+            type    => "m.room.name",
+            content => { name => "A room name" },
+         );
+      })->then( sub {
+         matrix_join_room_synced( $bob, $room_id );
+      })->then( sub {
+         matrix_join_room( $charlie, $room_id );
+      })->then( sub {
+         matrix_sync( $alice, filter => $filter_id );
+      })->then( sub {
+         my ( $body ) = @_;
+         log_if_fail ( "sync response:", $body->{rooms}{join}{$room_id} );
+         my $summary = $body->{rooms}{join}{$room_id}{summary};
+         assert_deeply_eq($summary, {
+            'm.joined_member_count' => 3,
+            'm.invited_member_count' => 0,
+         });
+         Future->done(1);
+      });
+   };
+
+
+test "Room summary only has 5 heroes",
+   requires => [ local_user_fixtures( 6 ),
+                 qw( can_sync ) ],
+
+   check => sub {
+      my ( $alice, @users ) = @_;
+
+      my ( $filter_id, $room_id );
+
+      matrix_create_filter( $alice, {
+         room => {
+            state => {
+               lazy_load_members => JSON::true
+            },
+         }
+      } )->then( sub {
+         ( $filter_id ) = @_;
+
+         matrix_create_room_synced( $alice );
+      })->then( sub {
+         ( $room_id ) = @_;
+         repeat( sub {
+            matrix_join_room_synced( $_[0], $room_id );
+         }, foreach => [ @users ])
+      })->then( sub {
+         matrix_sync( $alice, filter => $filter_id );
+      })->then( sub {
+         my ( $body ) = @_;
+         log_if_fail ( "sync response:", $body->{rooms}{join}{$room_id} );
+         my $summary = $body->{rooms}{join}{$room_id}{summary};
+         my $expected_heroes = [
+            (sort(
+               $users[0]->user_id,
+               $users[1]->user_id,
+               $users[2]->user_id,
+               $users[3]->user_id,
+               $users[4]->user_id,
+            ))[0..4]
+         ];
+         log_if_fail( "expected_heroes:", $expected_heroes );
+         assert_deeply_eq($summary, {
+            'm.joined_member_count' => 6,
+            'm.invited_member_count' => 0,
+            'm.heroes' => $expected_heroes,
+         });
+         Future->done(1);
+      });
+   };
+
+# TODO: test that parted users don't feature in room summaries, unless everyone has left
+# TODO: check we receive room state for unknown hero mxids
+# TODO: check that room summary changes whenever membership changes