diff --git a/libs/sk_ps_discovery/src/lib.rs b/libs/sk_ps_discovery/src/lib.rs
index 12bc6c738d..c4c376705e 100644
--- a/libs/sk_ps_discovery/src/lib.rs
+++ b/libs/sk_ps_discovery/src/lib.rs
@@ -352,6 +352,7 @@ impl World {
             HashMap::with_capacity(self.nodes_timelines.len());
         let commit_lsns_iter = self.commit_lsns.iter().map(|(k, v)| (*k, *v));
         let attachments_iter = self.attachments.iter().map(|(k, v)| (*k, *v));
+        let remote_consistent_lsns_iter = self.remote_consistent_lsns.iter().map(|(k, v)| (*k, *v));
 
         let join = merge_join::inner_equi_join_with_merge_strategy(
             commit_lsns_iter,
@@ -359,20 +360,18 @@ impl World {
             |(tenant_timeline_id, _)| tenant_timeline_id.tenant_id,
             |(shard_attachment_id, _)| shard_attachment_id.tenant_id,
         );
-        for (l, r) in join {
-            let (tenant_timeline_id, commit_lsn): (TenantTimelineId, Lsn) = l;
-            let (tenant_shard_attachment_id, node_id): (TenantShardAttachmentId, NodeId) = r;
-
-            // TOOD three-way equi join
-            let timeline_attachment_id =
-                tenant_shard_attachment_id.timeline_attachment_id(tenant_timeline_id.timeline_id);
-            match self
-                .remote_consistent_lsns
-                .get(&timeline_attachment_id)
-                .cloned()
-            {
+        let join = merge_join::left_equi_join_with_merge_strategy(
+            join,
+            remote_consistent_lsns_iter,
+            |((ttid, _), _)| ttid.tenant_id,
+            |(tlaid, _)| tlaid.tenant_timeline_id.tenant_id,
+        );
+        for ((c, a), r) in join {
+            let (tenant_timeline_id, commit_lsn): (TenantTimelineId, Lsn) = c;
+            let (_, node_id): (TenantShardAttachmentId, NodeId) = a;
+            match r {
                 // TODO: can > ever happen?
-                Some(remote_consistent_lsn) if remote_consistent_lsn >= commit_lsn => {
+                Some((_, remote_consistent_lsn)) if remote_consistent_lsn >= commit_lsn => {
                     // this timeline shard attachment is already caught up
                     continue;
                 }
diff --git a/libs/utils/src/merge_join.rs b/libs/utils/src/merge_join.rs
index 1ccef533aa..cfb6d0bf3f 100644
--- a/libs/utils/src/merge_join.rs
+++ b/libs/utils/src/merge_join.rs
@@ -37,11 +37,65 @@ where
     })
 }
 
+pub fn left_equi_join_with_merge_strategy<L, LI, R, RI, K, FL, FR>(
+    l: L,
+    r: R,
+    key_l: FL,
+    key_r: FR,
+) -> impl Iterator<Item = (LI, Option<RI>)>
+where
+    L: Iterator<Item = LI>, // + Sorted
+    R: Iterator<Item = RI>, // + Sorted
+    FL: 'static + Fn(&LI) -> K,
+    FR: 'static + Fn(&RI) -> K,
+    LI: Copy,
+    RI: Copy,
+    K: PartialEq + Eq + Ord,
+{
+    let mut l = l.map(move |i| (i, key_l(&i))).peekable();
+    let mut r = r.map(move |i| (i, key_r(&i))).peekable();
+    let mut l_had_match = false;
+    std::iter::from_fn(move || {
+        loop {
+            match (l.peek(), r.peek()) {
+                (Some((_, lk)), Some((_, rk))) if lk < rk => {
+                    let (lv, _) = l.next().unwrap();
+                    if l_had_match {
+                        l_had_match = false;
+                        continue;
+                    } else {
+                        return Some((lv, None));
+                    }
+                }
+                (Some((_, _)), None) => {
+                    let (lv, _) = l.next().unwrap();
+                    if l_had_match {
+                        l_had_match = false;
+                        continue;
+                    } else {
+                        return Some((lv, None));
+                    }
+                }
+                (Some((_, lk)), Some((_, rk))) if lk > rk => {
+                    drop(r.next());
+                    continue;
+                }
+                (Some((lv, lk)), Some((_, rk))) => {
+                    l_had_match = true;
+                    assert!(lk == rk);
+                    let (rv, _) = r.next().unwrap();
+                    return Some((lv.clone(), Some(rv)));
+                }
+                (None, None) | (None, Some(_)) => return None,
+            }
+        }
+    })
+}
 #[cfg(test)]
 mod tests {
 
     #[test]
-    fn basic() {
+    fn inner_equi_basic() {
         let l = vec![b"a", b"c"];
         let r = vec![b"aa", b"ad", b"ba", b"bb", b"ca", b"cb", b"cd", b"dd"];
 
@@ -64,4 +118,47 @@ mod tests {
             ]
         );
     }
+
+    #[test]
+    fn left_equi_basic() {
+        /*
+        create table aleft (id text, aleft text);
+        create table aright (id text, aright text);
+        insert into aleft values ('a', 'a'), ('b', 'b');
+        insert into aright values ('a', 'aa'), ('a', 'ab'), ('c', 'cd');
+        select * from aleft left join aright using ("id");
+        */
+
+        let l = vec![b"a", b"b"];
+        let r = vec![b"aa", b"ab", b"cd"];
+
+        let res: Vec<_> = super::left_equi_join_with_merge_strategy(
+            l.into_iter(),
+            r.into_iter(),
+            |l| &l[0..1],
+            |r| &r[0..1],
+        )
+        .collect();
+
+        assert_eq!(
+            res,
+            vec![(b"a", Some(b"aa")), (b"a", Some(b"ab")), (b"b", None)]
+        );
+    }
+
+    #[test]
+    fn left_equi_basic_2() {
+        let l = vec![b"b"];
+        let r = vec![b"aa", b"ab", b"bb"];
+
+        let res: Vec<_> = super::left_equi_join_with_merge_strategy(
+            l.into_iter(),
+            r.into_iter(),
+            |l| &l[0..1],
+            |r| &r[0..1],
+        )
+        .collect();
+
+        assert_eq!(res, vec![(b"b", Some(b"bb"))])
+    }
 }