diff --git a/brozzler/frontier.py b/brozzler/frontier.py
index b199c1c9..e0edd6f8 100644
--- a/brozzler/frontier.py
+++ b/brozzler/frontier.py
@@ -51,16 +51,18 @@ def filter_claimable_site_ids(
         ):
             is_claimable = True
 
-        # or site has been disclaimed more than an hour ago
+        # or site has been claimed more than an hour ago
         if "last_claimed" in site and site["last_claimed"] <= (
             now - datetime.timedelta(hours=1)
         ):
             is_claimable = True
 
-        # Count number of claimed sites per job_id (optional field)
+        # Count number of claimed sites per job_id (ignoring sites claimed over an hour ago)
+        # for enforcing the optional max_claimed_sites per job
         if site["claimed"] and "max_claimed_sites" in site and "job_id" in site:
-            job_id = site["job_id"]
-            job_counts[job_id] = job_counts.get(job_id, 0) + 1
+            if not is_claimable:
+                job_id = site["job_id"]
+                job_counts[job_id] = job_counts.get(job_id, 0) + 1
 
         if is_claimable:
             claimable_sites.append(site)
diff --git a/tests/test_frontier.py b/tests/test_frontier.py
index e030ffdc..b047923b 100644
--- a/tests/test_frontier.py
+++ b/tests/test_frontier.py
@@ -27,6 +27,7 @@
 
 import doublethink
 import pytest
+import rethinkdb as rdb
 
 import brozzler.cli
 
@@ -35,6 +36,7 @@
 args = arg_parser.parse_args([])
 args.log_level = logging.INFO
 brozzler.cli.configure_logging(args)
+r = rdb.RethinkDB()
 
 
 @pytest.fixture(scope="module")
@@ -953,10 +955,20 @@ def test_max_claimed_sites(rethinker):
     sites = list(frontier.job_sites(job.id))
     assert len(sites) == 5
 
-    claimed_sites = frontier.claim_sites(1)
-    assert len(claimed_sites) == 1
-    claimed_sites = frontier.claim_sites(3)
-    assert len(claimed_sites) == 2
+    claimed_sites_1 = frontier.claim_sites(1)
+    assert len(claimed_sites_1) == 1
+    claimed_sites_2 = frontier.claim_sites(3)
+    assert len(claimed_sites_2) == 2
+    with pytest.raises(brozzler.NothingToClaim):
+        frontier.claim_sites(3)
+
+    # if we "wait" an hour, we can reclaim
+    rr.table("sites").get_all(
+        r.args([item["id"] for item in (claimed_sites_1 + claimed_sites_2)])
+    ).update({"claimed": True, "last_claimed": r.now().sub(61 * 60)}).run()
+
+    claimed_sites_3 = frontier.claim_sites(3)
+    assert len(claimed_sites_3) == 3
     with pytest.raises(brozzler.NothingToClaim):
         frontier.claim_sites(3)