diff --git a/datasette/utils/__init__.py b/datasette/utils/__init__.py
index 490b71c8..f1c24041 100644
--- a/datasette/utils/__init__.py
+++ b/datasette/utils/__init__.py
@@ -171,7 +171,26 @@ allowed_sql_res = [
     re.compile(r"^explain with\b"),
     re.compile(r"^explain query plan with\b"),
 ]
-disallawed_sql_res = [(re.compile("pragma"), "Statement may not contain PRAGMA")]
+allowed_pragmas = (
+    "database_list",
+    "foreign_key_list",
+    "function_list",
+    "index_info",
+    "index_list",
+    "index_xinfo",
+    "page_count",
+    "max_page_count",
+    "page_size",
+    "schema_version",
+    "table_info",
+    "table_xinfo",
+)
+disallawed_sql_res = [
+    (
+        re.compile("pragma(?!_({}))".format("|".join(allowed_pragmas))),
+        "Statement may not contain PRAGMA",
+    )
+]
 
 
 def validate_sql_select(sql):
diff --git a/tests/test_utils.py b/tests/test_utils.py
index fe5d9a26..7e4f1a8e 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -140,7 +140,8 @@ def test_custom_json_encoder(obj, expected):
         "update blah;",
         "-- sql comment to skip\nupdate blah;",
         "update blah set some_column='# Hello there\n\n* This is a list\n* of items\n--\n[And a link](https://github.com/simonw/datasette-render-markdown).'\nas demo_markdown",
-        "PRAGMA case_sensitive_like = true" "SELECT * FROM pragma_index_info('idx52')",
+        "PRAGMA case_sensitive_like = true",
+        "SELECT * FROM pragma_not_on_allow_list('idx52')",
     ],
 )
 def test_validate_sql_select_bad(bad_sql):
@@ -162,6 +163,8 @@ def test_validate_sql_select_bad(bad_sql):
         "WITH RECURSIVE cnt(x) AS (SELECT 1 UNION ALL SELECT x+1 FROM cnt LIMIT 10) SELECT x FROM cnt;",
         "explain WITH RECURSIVE cnt(x) AS (SELECT 1 UNION ALL SELECT x+1 FROM cnt LIMIT 10) SELECT x FROM cnt;",
         "explain query plan WITH RECURSIVE cnt(x) AS (SELECT 1 UNION ALL SELECT x+1 FROM cnt LIMIT 10) SELECT x FROM cnt;",
+        "SELECT * FROM pragma_index_info('idx52')",
+        "select * from pragma_table_xinfo('table')",
     ],
 )
 def test_validate_sql_select_good(good_sql):