diff --git a/compute/etc/sql_exporter/db_total_size.sql b/compute/etc/sql_exporter/db_total_size.sql
index 9cbbdfd8a3..fe0360ab5c 100644
--- a/compute/etc/sql_exporter/db_total_size.sql
+++ b/compute/etc/sql_exporter/db_total_size.sql
@@ -1 +1,5 @@
-SELECT sum(pg_database_size(datname)) AS total FROM pg_database;
+SELECT sum(pg_database_size(datname)) AS total
+FROM pg_database
+-- Ignore invalid databases, as we will likely have problems with
+-- getting their size from the Pageserver.
+WHERE datconnlimit != -2;
diff --git a/compute/etc/sql_exporter/pg_stats_userdb.sql b/compute/etc/sql_exporter/pg_stats_userdb.sql
index 00ada87370..12e6c4ae59 100644
--- a/compute/etc/sql_exporter/pg_stats_userdb.sql
+++ b/compute/etc/sql_exporter/pg_stats_userdb.sql
@@ -1,10 +1,20 @@
 -- We export stats for 10 non-system databases. Without this limit it is too
 -- easy to abuse the system by creating lots of databases.
 
-SELECT pg_database_size(datname) AS db_size, deadlocks, tup_inserted AS inserted,
-  tup_updated AS updated, tup_deleted AS deleted, datname
+SELECT pg_database_size(datname) AS db_size,
+  deadlocks,
+  tup_inserted AS inserted,
+  tup_updated AS updated,
+  tup_deleted AS deleted,
+  datname
 FROM pg_stat_database
 WHERE datname IN (
   SELECT datname FROM pg_database
-  WHERE datname <> 'postgres' AND NOT datistemplate ORDER BY oid LIMIT 10
+  -- Ignore invalid databases, as we will likely have problems with
+  -- getting their size from the Pageserver.
+  WHERE datconnlimit != -2
+    AND datname <> 'postgres'
+    AND NOT datistemplate
+  ORDER BY oid
+  LIMIT 10
 );